Police accuse Mr Biti of inciting violence following last month’s election – the first since long-time ruler Robert Mugabe was ousted.
Six people were killed after the military intervened to curb protests in the capital, Harare.
The MDC Alliance alleges the presidential poll was rigged.
But the electoral commission disputes this and says incumbent President Emmerson Mnangagwa, who took over from Mr Mugabe, won the election.
He took 50.8% of the votes cast, ensuring by only 36,464 ballots that there did not have to be a run-off.
The opposition says its candidate, Nelson Chamisa, was the victor and the results were manipulated.
It has confirmed that it will challenge the result in court. An MDC Alliance lawyer, Thabani Mpofu, was quoted by AFP news agency as saying the official outcome had been a “total negation of the will of the people”.
Mr Biti was trying cross into Zambia to seek asylum when he was arrested, said his lawyer, Nqobizitha Mlilo.
He is the first senior politician to be arrested following July’s election – and was minister of finance in a unity government formed after disputed elections in 2008.
Mr Biti is credited with helping stabilise the economy after years of hyperinflation.
His arrest warrant, seen by the BBC, says Mr Biti “unlawfully” announced that Mr Chamisa had won the presidential election.
MDC Alliance Senator David Coltart called his arrest “utterly appalling”.
“I see all the tactics of Mugabe and all the tactics used by this regime for the last 38 years,” he told the BBC.
Altogether the police are hunting for nine senior opposition officials.
July’s elections were intended to set Zimbabwe on a new democratic path after the end of Mr Mugabe’s 37-year rule last November.Post published in: Featured