The band, led by Neil Finn, had been due to appear at Utilita Arena in the city centre on June 11.
The tour has now been resceduled for 2022 with the Birmingham date now June 14.
Tickets, which cost £40.75, already purchased are valid for the new date.
Crowded House, which originally formed in Australia in 1985, has had a strong of hit singles and albums over the years.
The band's seventh studio album, Dreamers Are Waiting, is due for release on June 4 this year.