The senator was not hurt but two airbags deployed during the collision, according to Marc Roy, the director of communications for the Liberal leader in the Senate.
Dallaire's single vehicle accident occurred after he passed the RCMP checkpoint, an entrance all parliamentarians must use to enter and exit the grounds on Parliament Hill.
The Senator nodded off from sheer exhaustion because he had not slept last night, Roy said.
Dallaire's black BMW skidded off the road, past the sidewalk and onto the snow-covered grass before hitting the lamp post on Parliament Hill.
The RCMP closed the road to traffic while Dallaire's car was towed.
Dallaire is a retired general who has battled post-traumatic stress disorder after heading up the ill-fated UN peacekeeping mission in Rwanda.
The senator will be at work and report to the upper chamber this afternoon, Roy said.
RCMP say that "like alcohol, fatigue impairment slows reaction time, decreases awareness, impairs judgment and increases the risk of crashing."