Police initially said that business rivalry was a more likely motive for the attack on the Movida bar restaurant outside Kuala Lumpur on 28 June.
They added that two men suspected of involvement had been arrested.
Authorities are increasingly concerned about IS-related attacks as a number of Malaysians have gone to fight in Syria.
"There were elements of IS involvement in the attack," national police chief Khalid Abu Bakar told reporters.
"We found out that the two of them received instructions from one of our own citizens in Syria... to conduct attacks in Malaysia."
There have been dozens of extremism-related arrests in recent years, including 13 Malaysians detained following the latest attack but who police said were not directly connected to it.
Governments across the region have warned of an increased threat from the group.

The cabinet considered an urgent report on Tuesday and voted to remove the section from the pavilion to the seaward end.
The report said because of the risk of further collapse, the council could not wait for consent to begin work, as is usually the case for a listed building.
Work on the "dangerous" structure is expected to take about three weeks.
Parts of the Grade ll pier, which was already closed to the public when it gave way on 1 February, will be saved, catalogued and stored.
Iwan Davies, chief executive of the council, told the meeting: "The dangerous nature of the structure means dismantling it is dangerous."
Up to Â£650,000 has been set aside for the work but councillors were told there was no way of knowing how much it would cost.

The quartet of Allison Schmitt, Leah Smith, Maya Dirado and Ledecky won in a time of seven minutes 43.03 seconds, with Australia second and Canada third.
America trailed Australia but Ledecky, the 200m and 400m freestyle champion, overtook Tamsin Cook on the last leg.
Find out how to get into swimming with our special guide.
Ledecky, 19, has now won four Olympic gold medals during her career.
Her first Olympic gold came when she won the 800m title as a 15-year-old at London 2012.
Ledecky will attempt to complete the sweep when she goes in the 800m heats on Thursday, with the final taking place on Friday.
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Allardyce took charge of the Black Cats in October when they were winless in their opening eight matches, but guided them to 17th and safety.
"I don't want to go through that again," he told BBC Newcastle.
Allardyce added that he plans to discuss transfer targets with owner Ellis Short in the next few days.
Sunderland survived with a game to spare after victory over Everton with Allardyce describing it as a "miraculous achievement."
However the former West Ham and Bolton boss, who has never been relegated, says the club must learn from its mistakes this campaign.
"Our season has been a difficult one. I don't want to go through that again - that's the most important thing for me, not to put myself through what I did to get where we are today," he added.
"The turnaround has given me great satisfaction. It hasn't made me forget about when it was tough, and we have to make sure it doesn't happen again."
Sunderland ended the season with only one defeat in 11 games, and were unbeaten in their last six.
Allardyce plans to discuss summer signings with Short when he is back from a mini-break - a meeting that "will be one of great importance" according to the the 61-year-old.
"We will have a couple of days off and then see what the situation is," Allardyce said.
"I can't look or see in to the future. It looks very positive but until we need to get down and talk about it. Then we can move forward."
Malaysian police have said a blast at a bar last week, which injured eight, was the first attack by the so-called Islamic State group in the country.
[NEXT_CONCEPT]
Part of Colwyn Bay pier is to be dismantled after it collapsed into the sea, Conwy council has decided.
[NEXT_CONCEPT]
Katie Ledecky won her third gold of the Rio Games as she guided the United States to victory in the women's 4x200m freestyle relay final.
[NEXT_CONCEPT]
Sunderland manager Sam Allardyce says he is determined to make sure the club is not involved in another Premier League relegation fight next season.