Trudi Rishikof, 64, was hit by the 4x4 in the US capital in October.
Swiss media named the driver as Kamal Mortada, a former employee of Hannibal Qaddhafi, son of the ousted Libyan leader.
The victim's widower Harvey Rishikof, a specialist in national security law and terrorism at Washington's National War College, is seeking $10 million, Swiss newspaper Blick reported.
Mortada was at the centre of diplomatic row between Libya and Switzerland in 2008 when he reported his employer to Geneva police for ill-treatment.
According to Blick, Mortada had since turned up in Washington where he was working for the Swiss embassy.
The complaint was filed in the capital a week ago against Mortada and the Swiss embassy, citing reckless driving, it reported.
The foreign ministry confirmed in October that a local embassy employee was involved in a fatal car accident in Washington but said on Thursday it had not been informed of the complaint.