The ruling party counted the cars a month after taking power following victory in December's elections.
After previous transfers of power, state-owned cars have been seized from officials who did not return them.
A minister in the former government said the implied allegation of wrongdoing by his colleagues was false.
Former Communication Minister Omane Boamah told the BBC's Thomas Naadi that this was "a convenient way for the new government to justify the purchase of new vehicles".
Presidential spokesman Eugene Arhin told the press that officials could only find:
74 of the presidency's 196 Toyota Land Cruisers
20 of the 73 Toyota Land Cruiser Prados
11 of the 24 Mercedes
2 of the 28 Toyota Avalons
2 of the six BMWs.
Ghanaian radio station Citi FM reported that the president has been "forced to use a 10-year-old BMW" as a result.
In making the statement Mr Arhin revealed the president's office was meant to have more than 300 cars but he did not divulge the purpose of these vehicles.
Nana Akufo-Addo from the the New Patriotic Party won the Ghanaian presidential election at the beginning of December, taking power from John Mahama, of the National Democratic Congress.