According to Iranian media reports, four people have been identified in connection with the couple's death.
Mehrjuyi was considered one of the founders of Iranian new wave cinema.
According to court president Hossein Fazeli, the couple invited their daughter Mona Mehrjuyi to their home in the city of Keraj, 30 kilometers from Tehran, for dinner on Saturday evening.
The couple's bodies were discovered by the daughter when she came home for dinner.
Mohammadifar reportedly complained that he had recently been threatened and that their house had been robbed.
Iranian authorities said Mehrjuyi, 83, and his wife were stabbed in their home.
Iranian actor and director Houman Seyedi reacted to the killings on social media, describing them as "horrific and brutal".
Mehrjuyi studied in the United States as a young man and later lived in France for five years. His 1969 film The Cow brought him national and international attention for the first time.
Hamoun, The Pear Tree and Leila are also among Mehrcuyi's notable films.
Although the New Wave movement focused mostly on realism, Mehrcuyi was known to be inspired by literature.
Mehrcuyi received numerous awards, but some of his films could not be screened in his country due to censorship.