Radiohead were due to play two dates at the venue on 4 and 5 July - but will now play a single night at Old Trafford cricket ground on 4 July instead.
Celine Dion's shows on 25 June and 1 August have been postponed.
Ritchie Blackmore's Rainbow, Key 103 Live and PAW Patrol Live! in June, July and August have all been cancelled. No reopening date has been announced.
The next events in the diary are Linkin Park on 7 July and Blink-182 on 14 July. The arena has not commented on the status of those shows but they must too be in doubt.
Fans with tickets to Radiohead's arena shows can either swap them for the new stadium gig or get a full refund.
Extra tickets for the Old Trafford show will go on sale on Saturday. A statement from the promoter said: "The group apologise to fans for any inconvenience."
Twenty-two people died in the bombing at the end of an Ariana Grande concert at the arena on 22 May.
In a statement, the arena said the latest shows had been put off "following last month's tragic incident and the subsequent temporary closure of the main area outside the venue".
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Concerts by Celine Dion and Radiohead at Manchester Arena have been moved or postponed after last month's attack.