The full-back – on loan from Real Madrid – came on as a substitute to replace the injured Abdou Diallo in the 49th minute but then had to be replaced himself with 16 minutes remaining.
He will now miss the club's remaining Bundesliga fixtures – including Saturday's pivotal clash against title rivals Bayern Munich – and faces a race to be fit for Morocco's Africa Cup of Nations campaign.
Hakimi has featured 28 times for Lucien Favre's side in all competitions this term, scoring three goals and recording seven assists.
Primarily a right-footed player, he has played in both full-back positions with regularity and his absence is a real blow for Dortmund in terms of cover in the wide defensive areas.
With Lukasz Piszczek also out injured, the club find themselves desperately short at right-back in particular, and a centre-back may be forced to play out of position there for an extended period.
Achraf Hakimi will miss the for the rest of the season due to a broken metatarsal.— Borussia Dortmund (@BlackYellow) April 1, 2019
Wishing you a speedy recovery, Achraf! pic.twitter.com/DDiQGXIre3
The club also confirmed that Diallo suffered a muscle strain but have not specified how long he will be out of action.
The pair join Christian Pulisic and Maximilian Phillipp - as well as the aforementioned Piszczek - on the treatment table as the strain of the season start's to take its toll on the Dortmund squad.
Dortmund go into the game against Bayern two points ahead of their opponents after Niko Kovac's side drew 1-1 with Freiburg at the weekend.
Der Klassiker may well decide the league title, as Bayern suffered a poor start to the campaign that allowed Dortmund to take an early advantage, but a late surge from the reigning champions has seen the title race become neck-and-neck.
Dortmund won the reverse fixture 3-2 at home as a late Pace Alcacer strike settled the game after Marco Reus and Robert Lewandowski both hit doubles.