Saudi clubs have refused to play in Iran since the kingdom broke off relations in January 2016 forcing AFC Champions League fixtures with Iranian clubs to be played in neutral Oman.
"It's very clear that politics should stay out of football and football should stay out of politics," Infantino said at a joint news conference in Tehran with Iranian Sport Minister Massoud Soltanifar.
"There are of course political issues between countries all over the world but this should not have an impact on the football tournament.
The FIFA chief acknowledged that Saudi Arabia had voiced security concerns after protesters angry at its execution of a top Shiite cleric attacked its embassy and a consulate in Iran, prompting it to cut ties.
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"Obviously the guarantees must be there, the safety must be there," he said.
The Iranian minister denied there were any legitimate security concerns.
"Iran is a totally safe country," he said, while welcoming "FIFA's non-political approach".
"We asked (Infantino) to insist on that so we can host games in the normal way from the next round and our clubs will not be forced to go to third countries to be able to play," Soltanifar said.
The FIFA president then went to watch a derby match between Tehran rivals Persepolis and Esteghlal.