Doctors say that Bickauskas suffered an epileptic fit brought on by a concussion.
On the afternoon of Jan. 31, Bickauskas' Land Rover ran into a parked car on one of the busiest streets in Vilnius and then quickly left the scene of the accident, police said. But the Land Rover left behind its special parliamentary license plates.
Police used the plates to track Bickauskas down, but he refused to allow them to examine his jeep.
A decision about a fine will be made in the next few days. Bickauskas could get a fine and be stripped of his driver's license for leaving the scene of the accident.
In his explanation to the traffic police, the ex-parliamentarian admitted that he drove the Land Rover and left the crash scene before the police were able to get there.
Bickauskas' blood alcohol levels were not checked.
A Foreign Ministry spokesman announced that Foreign Minister Antanas Valionis has requested that an investigation be conducted into the incident to collect all related information.
Valionis has vowed to decide on Bickauskas' future immediately after receiving the conclusions of the analysis. The minister has said that everybody is equal under the law, adding that the Foreign Ministry will not tolerate any violations of the law.
A household name in Lithuania, Bickauskas is a signatory of the March 11, 1990 Independence Act and a former member of Parliament.
After completing three four-year terms in the Parliament, he lost his seat after last October's general elections and later took the position at the Foreign Ministry.