Hepworth will focus on its Honda outlets in Huddersfield and Halifax.
The former Mitsubishi site at Huddersfield may be let as a garage, or possibly redeveloped if planning permission is granted.
The future for the leasehold Bradford site, acquired from Sunwin Group in 2003, has not yet been decided.
The closures will reduce Hepworth’s turnover from £30m in 2006 to around £18m this year.
Richard Weller, Mitsubishi UK network development general manager, says: “There were some concerns over the performance at the Bradford dealership, but the decision to close both was Hepworth’s.”
Weller says Mitsubishi is writing to all customers to advise them of Mitsubishi dealers in neighbouring territories who will be able to look after their vehicles until new dealers are appointed.
Stephen Brighton, group operations director, said Hepworth would now concentrate on its Honda businesses, and hoped in time to acquire another dealership with the franchise.