On Tuesday, the English top-flight said it would stop individuals from featuring for countries on the UK government's red list, meaning a quarantine on return, for September's matches.
Liverpool's Egypt forward Mohamed Salah and Manchester City's Brazil forward Gabriel Jesus are likely to miss out.
Spain's La Liga said it would back its clubs in stopping players from leaving during the windows in September and October.
"I am calling on a show of solidarity from every member association, every league, and every club, to do what is both right and fair for the global game," he said in a statement.
"Many of the best players in the world compete in leagues in England and Spain, and we believe these countries also share the responsibility to preserve and protect the sporting integrity of competitions around the world," he added.
Infantino said he had contacted British authorities after England loosened Covid-19 regulations during Euro 2020 in June and July.
"I have written to Prime Minister Boris Johnson and appealed for the necessary support, in particular, so players are not deprived of the opportunity of representing their countries in qualifying matches for the FIFA World Cup," he said.
"I have suggested that an approach similar to that adopted by the UK government for the final stages of the Euro 2020 be implemented for the upcoming international matches.
"Now, I am urging everyone to ensure the release of international players for the upcoming FIFA World Cup qualifiers."
Also on Tuesday, the English Football League, who control the second to the fourth tier of the sport, also said it would stop players from representing their countries.
"Discussions had taken place between the Government, FA and FIFA in an effort to find a solution, but due to ongoing public health concerns relating to incoming travellers from red-list countries, no exemption has been granted," the EFL said.
"Given there would be a requirement to quarantine for 10 clear days upon return from a red-list country, the potential impact on players are numerous with considerations relating to health and well-being along with unknown risks relating to COVID-19 transmission," it added.