The 31-year-old was named the man of the series as England stormed to an unprecedented 3-0 whitewash away to the Wallabies, despite missing the third Test due to the injury.
Haskell will now face reconstructive surgery on his big toe before returning to Wasps to complete his recovery.
"We're all really disappointed for James and we are all wishing him a speedy recovery," Wasps director of rugby Dai Young said in a statement.
"James's performances with England, both in the 3-0 series win over Australia and in England's Six Nations Grand Slam success, have been hugely impressive. Everyone at Wasps knows how hard James works to make those performances happen, and we know he'll be working just as hard to come back in the best shape possible.
"Our medical team will be working closely with James over the next few months to get him back to full fitness and in the meantime there will be a good opportunity for the other back-row players we have at the club to stake a claim."
The injury means that Haskell will miss the start of the 2016-17 Aviva Premiership season and may not return until next year.