A security official, speaking on condition of anonymity, said the policemen had been injured by members of the southern separatist movement.
"The three policemen were wounded in Dhale city. The three assailants are known to us and security forces are chasing them," he told the AFP newsagency.
'Act of disobedience'
Al Jazeera's Mohamed Vall, reporting from Sanaa, said the strike had been called by the Southern Movement as an "act of disobedience" in protest of the government not responding to their demands.
"The Southern Movement is made up of five groups. They call themselves the Supreme Council of for the Peaceful Revolution, but what heppened today was not quite peaceful.
"Some sporadic clashes happened, particularly in the areas of Dhale and Lahaj."
Abdo al-Maatari, one of the leaders of the separatist movement in the south, said ahead of the strike that the half-day protest was against "central government oppression" and would be peaceful.
"This protest confirms that we are adopting civilised and peaceful means with regards to the issue of the south," he told the AFP news agency.
South Yemen was an independent state from the time of Britain's withdrawal in 1967 until the country was united in 1990. The south seceded in 1994, sparking a short-lived civil war that ended with the region overrun by northern troops.
Separatists who want to end the north-south union are demanding independence in response to what they say is discrimination by northerners and a lack of financial aid.