Former leader Sali Berisha of the main opposition Democratic Party has created a grouping trying to move the party leader Lulzim Basha from the post, accusing him of being a "hostage" of Prime Minister Edi Rama of the Socialist Party.
"Today the Democrats and Albania's democrats will turn the bunker of hostage (Lulzim) Basha into their house of freedom," Berisha said.
Protesters stormed the ground floor of the building, using iron bars to open the main door and breaking windows.
Tear gas was used from inside the building to move them away.
At least one injured person was seen.
Following a request from the Democratic Party, police intervened using a water cannon truck and anti-riot police officers to push protesters away from the building.
Some protesters were taken away, detained by police.
"Today's acts of violence against the Democratic Party mark Sali Berisha's final isolation and a shameful move out of the political scene," a party statement said.
Basha fired Berisha from the parliamentary group in September, which sparked an internal party fight between them.
That followed an intervention in May by US Secretary of State Antony Blinken, who said in a statement that during Berisha's 2005-2013 tenure as prime minister, the politician "was involved in corrupt acts... using his power for his own benefit and to enrich his political allies and his family members," interfering in "independent investigations, anti-corruption efforts, and accountability measures".
Blinken said that Berisha's "corrupt acts undermined democracy in Albania".
In December Berisha's grouping claimed to have held a referendum removing Basha from his post but the move was not recognised by the official Democratic Party.
Berisha, 77, served as Albania's prime minister from 2005 until 2013 and as president from 1992-1997.
He was re-elected as an MP for the Democratic Party in last April's parliamentary election.
US ambassador in Tirana Yuri Kim expressed concern at the "rising tensions" at the Democrats' building and called on protesters "to reject violence and exercise calm".
"Those inciting violence or undermining the rule of law will be held accountable," she posted in Twitter.
Last month US Deputy Assistant Secretary of State Gabriel Escobar said there would be "consequences" if the Democratic Party chose someone to be leader who had been designated persona non grata by the US.
Berisha is the fourth top Albanian official to be barred from entering the United States because of alleged involvement in corruption.
Fighting corruption has been post-communist Albania's Achilles' heel, strongly affecting the country's democratic, economic and social development.
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