Waseem Akhtar, a member of the Muttahida Qaumi Movement (MQM) party, was elected mayor of Karachi in December but has not yet taken office due to delays in finalising local council elections in a couple of areas of the city.
Saqib Ismail, a senior police officer in Karachi, told Reuters Akhtar and another MQM member, Rauf Siddiqui, were arrested on suspicion of sheltering and providing medical treatment to alleged militants and criminals.
Ismail added that Anis Kaimkhani from the Pak Sarzameen Party was also arrested in Karachi, a teeming metropolis of about 20mn people.
"All three accused will be shifted to Central Jail," said Ismail, adding that police were conducting raids to arrest a fourth politician, Qadir Patel, who belongs to the Pakistan People's Party (PPP).
Party leaders were not immediately available to comment on the latest arrests but the lawyer of mayor-elect Akhtar told media he would challenge the arrests in court on Wednesday.
The arrests are part of an ongoing military-driven crackdown in Karachi and follow the high-profile arrest last year of Dr. Asim Hussain, a petroleum minister in a former PPP-led government.
Hussain is accused of harbouring and providing medical treatment to militants and criminals at his Karachi hospital on the behest of the three politicians arrested on Tuesday.
The latest arrests are likely to raise new accusations that Pakistan's powerful military is seeking to strengthen its grip on the country's largest and wealthiest city and weaken civilian parties.
Most of the hundreds of people targeted by paramilitary forces in recent months on accusations of political corruption and violence have belonged to the MQM. The PPP has in the past condemned Hussain's arrest and called it politically motivated.
The paramilitary Sindh Rangers have in the past said the Karachi crackdown is necessary to break the cycle of violence and corruption in a city that accounts for half of Pakistan's national revenues and hosts the stock exchange, central bank and two ports.