According to the party, Morgan Tsvangirai House was attacked by suspected ruling ZANU PF activists or state security agents.
“We certainly have a terrorist organisation in Zimbabwe, when they have a problem with managing the country, they burn HQs,” MDC presidential spokesman Nkululeko Sibanda wrote on Twitter.
He said the arson attack was carried out by individuals in unmarked vehicles.
The attack came as Zimbabweans braced for a second day of a countrywide protest over a hefty fuel price hike announced by President Emmerson Mnangagwa on Saturday.
Most people stayed at home on Tuesday as a tense atmosphere engulfed the capital Harare and other towns.
The usually bustling Harare central business district was deserted on Tuesday, with only security forces vehicles seen on the road.