The Glasgow Shettleston MSP was contacted by the Newcastle-based Celtic fan, who explained that he is unable to walk for more than 10 minutes.
The fan, who is a season ticket holder, expressed concern that a parking ban for match days at Celtic Park would mean he was unable to attend matches.
In an email, Mr Mason said: “Could you think about supporting a smaller more local club that would appreciate your adding to their crowd?”
Mr Mason is a Clyde supporter.
Labour MSP James Kelly said Mr Mason had made an “outrageous comment”.
Mr Kelly said: “Rather than representing the interests of a disabled man who wants to bring his custom and spend his money in John Mason’s constituency, he is just telling him to go support another football team.
“It’s a ludicrous response from a politician who has been a constant source of embarrassment for the SNP.
Mr Kelly added: “If John Mason’s attitude is to tell people to stay away from the East End of Glasgow he’ll soon find the voters in Shettleston will send him packing too.”
Mr Mason said the email was only one part of a wide discussion. He said there was a “huge problem” with inappropriate parking around Celtic Park and he supported the council’s proposal to make the area a more controlled parking zone.
Mr Mason said: “In response to several folk raising the question of disabled fans or others who could not walk far, I have said that there is plenty of room for these fans to park if those who are able to walk 20 minutes would park further away in a more considerate manner.
“The parking problem is not caused by disabled fans. It is caused by perfectly able bodied fans (often with very expensive cars!) wanting to park as close as possible to Celtic Park (and I think the other major stadia in the City) with no regard for residents. I hope that clarifies my position.
“However, as a more general point, I am a Clyde supporter and would like to see more fans considering supporting smaller more local teams… like Clyde! (To be fair to the gentlemen I was chatting to on social media or email, he told me he does also support a local team, so well done to him.)”