The mouthy singer axed a show in New York City last Thursday but performed on The Today Show the following day.
Allen was due to begin her US tour proper in May at Everett Events Centre in Seattle on May 13.
However, owners of club First Avenue in Minneapolis, where the singer was due to play on May 24, said that the date is off and refunds are available for the gig.
Her next scheduled appearance in the US is at the Coachella Festival in California on April 29, although it is current unclear if this will take place.
US media report that no official reason or confirmation of the cancellations has been given, although newspaper reports in the UK suggest the singer is "homesick" and eager to return early.