McKinnon started her sports career after transitioning in 2012 and has been criticised by pressure groups and top sportswomen.
It is a human right to participate in sport. I don't think it's a human right to identify into whichever category you choose.'
Dr McKinnon announced she was transgender in 2012 and started competing in cycling events in 2016 - rapidly rising to the top of the sport.
Last year she broke her first record at the 200m sprint at last year's UCI Masters World Track Cycling Championship and also won the event in the 35-44 age bracket.
Dr McKinnon responded to Ms Wood's comments with a statement that revealed they have never competed against each other.
'We are either full and equal women, or not. We are'
In December last year Dr McKinnon clashed with women's tennis great Martina Navratilova who said that allowing transgender women to compete in sport against people born as women was 'insane' and 'cheating'.
McKinnon called her 'transphobic' and Navratilova responded: 'McKinnon has vigorously defended her right to compete, pointing out that, when tested, her levels of testosterone, the male hormone, were well within the limits set by world cycling’s governing body.
'Nevertheless, at 6ft tall and weighing more than 14 stone, she appeared to have a substantial advantage in muscle mass over her rivals.'
After last year's UCI Masters Track Cycling World Championships in Los Angeles, the third-place finisher, Jennifer Wagner, said losing to Dr McKinnon was 'unfair'.
McKinnon responded to point out that she and Wagner have raced 13 times in the past and Wagner beat her 11 times.
She said: 'At Masters Worlds, she beat me in the 500m TT. She beat me in six of seven races at the 2017 Intelligentsia Cup. In 2016 she beat me in all three Speed Week crits. She's won 11 of our 13 races.
'And it's unfair? Excuse me?'
In March this year Paula Radcliffe, who has held the Women's World Marathon Record since 2003, said: 'There are absolutely probably hundreds of transgenders who want to take part in sport for all of the other benefits that it brings.
'And all we’re saying is: ''That’s fine, but not elite sport''.'
McKinnon then accused Radcliffe of spreading 'irrational fear'.
Olympic swimmer Sharron Davies, who won silver in 1980, has also spoken out about transgender women being allowed to compete.
She said: 'I believe there is a fundamental difference between the binary sex you are born with and the gender you may identify as.
'To protect women’s sport, those with a male sex advantage should not be able to compete in women’s sport.'
McKinnon hit back at Davies by calling her a transphobe and accusing her of 'sharing hate speech'.
She said: 'There is no debate to be had over whether trans women athletes have an unfair advantage: it’s clear that they don’t.
'Since the Nov 2003 IOC policy openly allowing trans women to compete, not a single trans athlete has even qualified for the Olympics, let alone won a medal.'
Dame Kelly Holmes spoke out earlier this year against transgender women being allowed to compete against people who were born biologically female.
And in response McKinnon tweeted to call her 'extremely transphobic' before blocking the two-time Olympic gold medallist on Twitter.
Holmes responded by saying: 'If this subject is open to debate then why have I been blocked.
'As far as I am concerned you are going about this in the wrong way.
'Calling me transphobic is just ridiculous - far from it.
'I have an opinion you don’t like that’s that!'
British cyclist Victoria Hood continued her criticism of McKinnon by saying: 'The world record has just been beaten today by somebody born male, who now identifies as female, and the gap between them and the next born female competitor was quite a lot.
'The world record was two tenths of a second. I know that doesn't sound like a lot but it is.
Defending herself, McKinnon wrote: 'Many people claim to support trans women. But often they only support us until our lives impact them in any meaningful way.'
McKinnon (center) celebrates her gold medal on the podium with bronze medalist Kirsten Herup Sovang of Denmark and silver medalist Dawn Orwick (left) of the USA
McKinnon is pictured second from left with fellow athletes at the contest in Manchester
'The gap between them and the next female competitor was four tenths, which to put into perspective in a sprint event like this, that would be 15m of the track, when sprint events are usually won by centimetres.'
As well as releasing a statement which pointed out that her new record was still behind several others set by athletes who were born biological females, she also took to Twitter.
She wrote: 'Many people claim to support trans women. But often they only support us until our lives impact them in any meaningful way.
'In my case, people literally say they support trans women... but not in sport.
'There can be no ''but''.
'We are either full and equal women, or not. We are.'
Transgender athletes have been allowed to compete in the Olympics since 2004 if they have undergone gender confirmation surgery and been on hormone therapy for two years.
In 2015, these rules were relaxed to remove the need for surgery and athletes must now have a testosterone level below 10nmol/L for at least 12 months prior to their first competition.
Athletics' governing body the IAAF had the same requirements until last Monday when they announced that female athletes must have a testosterone level below 5nmol/L.
McKinnon, an assistant professor of philosophy, beat American Dawn Orwick for this year's title.
What titles has transgender Canadian cyclist Dr Rachel McKinnon won since her foray into the sport?