Infantino met President Joko Widodo in the capital Jakarta, a year before the Under-20 World Cup is due to be held in the Southeast Asian nation.
"We will reform and transform football in this country", Infantino said, flanked by Widodo.
His assurances came as hospital officials said a 33-year-old man had died from injuries sustained in the Kanjuruhan stadium crush, bringing the confirmed death toll to 133.
More than 40 children were among those killed in the city of Malang, East Java on October 1, in what Infantino described as "one of the darkest days for football".
After supporters invaded the pitch at the end of a league match between Arema FC and rivals Persebaya Surabaya, police fired tear gas into packed stands, sparking a stampede.
"What I can guarantee to all the people of Indonesia: FIFA is here with you, FIFA is here to stay, FIFA is here to work in a very close partnership with the government, with the Asian Football Confederation and with the federation of Indonesia," Infantino said after meeting Widodo.
The main focus would be improving stadium operations and fan behaviour, Infantino said, as well as creating programmes for football in schools.
"We will bring our experts, we will help and invest and we will make sure that Indonesia shines on the global football stage," he added.
Widodo said he agreed with FIFA "on a thorough transformation of Indonesian football to ensure all aspects of the matches follow the international safety standards set up by FIFA".
"The safety for both the players and fans must be guaranteed," he said.
Infantino said FIFA would work with the Indonesian government to ensure the Under-20 World Cup can go ahead safely.
The youth tournament is scheduled to take place in May-June 2023, in multiple cities across the archipelago nation.
Three police officers are among six people who have been charged over the tragedy.
An investigating task force has called on the country's football association chief and all of its executive committee members to resign.
It also found that more than three hours of footage from CCTV in the main lobby and parking area of the stadium had gone missing.
Representatives from FIFA and the Asian Football Confederation (AFC) have been in Jakarta since last week to investigate what happened, along with the national FA and the government.
Widodo has suspended all football matches until the investigation is complete and ordered a safety review of all stadiums.
