The stampede at Kanjuruhan Stadium is one of the worst in a tragically long line of stadium disasters
About 180 people were also hurt after Arema FC's loss to rivals Persebaya Surabaya in East Java on Saturday.
The crush took place after police tear-gassed fans who invaded the pitch.
"The football world is in a state of shock following the tragic incidents that have taken place in Indonesia," Infantino said.
"This is a dark day for all involved in football and a tragedy beyond comprehension."
As panic spread in Kanjuruhan Stadium in Malang, thousands surged towards the exits, where many suffocated.
Fifa, the world's governing football body, states that no "crowd control gas" should be carried or used by stewards or police at matches.
Infantino added: "I extend my deepest condolences to the families and friends of the victims who lost their lives following this tragic incident.
"Together with Fifa and the global football community, all our thoughts and prayers are with the victims, those who have been injured, together with the people of the Republic of Indonesia, the Asian Football Confederation, the Indonesian Football Association, and the Indonesian Football League, at this difficult time."
The head of the Asian Football Confederation, Sheikh Salman bin Ebrahim Al Khalifa, told Reuters in a statement he was "deeply shocked and saddened to hear such tragic news coming out of football-loving Indonesia".
La Liga and the Spanish Football Federation (RFEF) have agreed that clubs will observe a minute's silence before kick-off in Sunday's games as a mark of respect.
A statement by La Liga said the silence would "offer condolences to the Indonesian people, especially the families of the deceased, as well as wishing a quick recovery to those injured".
Players wore black armbands in Sunday's two Premier League matches, and several clubs offered their condolences to the victims of the disaster.
Liverpool tweeted: "We are deeply saddened to hear of the events at Kanjuruhan Stadium, Malang, Indonesia. The thoughts of everyone at Liverpool Football Club are with all those affected at this time."
In the UK, a crush developed at the Hillsborough Stadium in Sheffield in 1989, resulting in the deaths of 97 Liverpool fans attending the club's FA Cup semi-final against Nottingham Forest.
England captain Leah Williamson posted on Twitter: "My thoughts are with everyone affected by this tragedy. Indonesia holds a special place in my heart."
Spain defender Sergio Ramos called the incident "heartbreaking" while ex-England forward Wayne Rooney said it was "devastating".
Ajax's club account tweeted: "We are deeply saddened by the tragedy in Malang, Indonesia. There should never be violence at a football match."
Barcelona said they were "pained by the tragic events" at Kanjuruhan Stadium, adding they "reject all acts of violence both on and off the field".
-- Courtesy of BBC Sport