Infantino said if there is racism in the stands at matches, the first sanction for clubs will no longer just be a fine but a partial stadium closure. If there is more racism in the stands, Infantino said there will be a "full closure of the stadium and a minimum fine of $65,500."
UEFA wants to double the current minimum ban of five matches that players and officials currently face for racial abuse.
The UEFA executive committee will be asked next month to give final approval for punishments. While UEFA can only enforce the punishments in its competitions, UEFA's 53 members will be asked to adopt the same measures.
"We just felt it's time to send out a strong message," Infantino said.
The debate on racism intensified this season after AC Milan midfielder Kevin-Prince Boateng led his team off a field during an exhibition in Italy after facing abuse from fans.
UEFA has been criticized in the past for only fining national associations for racist abuse by fans.
In England in recent years, Liverpool striker Luis Suarez received an eight-match ban for racially abusing an opponent and Chelsea captain John Terry was suspended for four matches.
"We have to have sanctions and they must have a deterrent effect," Infantino said.
On Wednesday, UEFA ordered Dynamo Kiev to play a European club competition match next season in an empty stadium because of racist conduct by its supporters during home matches in the Champions League and Europa League.