Warning of the risk posed by the Delta variant, he asked supporters not to gather in the capital.
He said Scotland supporters will not be able to access their traditional meeting spot of Trafalgar Square as it will be used as a socially-distanced, ticketed fan zone for key workers, and pubs will have limited space due to coronavirus measures.
Mr Khan said: “It is absolutely fantastic that Scotland are playing in their first international tournament for 23 years and I cannot wait for Friday’s match.
“Scottish fans are renowned around the world for bringing a party atmosphere with them to the big tournaments but with Covid restrictions still in place on both sides of the border, the best thing for fans without tickets to the game or a safe place to watch it is to enjoy the game from Scotland and not come to London.
“In an ideal world I would welcome the Tartan Army to London for this match with open arms, but with Covid cases increasing, and with so much at stake as we fight this awful virus, I’m afraid that it just cannot be this time, so the best thing to do is not to come to London and instead enjoy the game at home.”
Scottish culture minister Jenny Gilruth backed the plea, as she said a cautious approach to celebrating the much-anticipated game is needed.
“I strongly urge fans to only travel if you have a ticket or a safe place to watch the match from,” she said.
“Although we have made great progress, we all still have an important part to play in making sure we keep the virus under control. So I urge all football fans to plan in advance how you are going to safely enjoy the tournament.”