The arrested have been identified as Pervaiz Ahmad Ganie, his cousin Aijaz Ahmad, and Riyaz Ahmad Wani.
The fourth accused Muzaffar Ahmad in the case is still absconding and efforts are on to nab him, police said.
The oil tanker was recovered by police from Pulwama district on June 24, a day after the body of the driver Akshay Kumar Sharma was found in Qazigund, 80 km from here, in Anantang district, they said.
Sharma had left for Kashmir with fuel on June 22 but went missing en route, police said, adding that since the identity of the driver could not be established immediately, he was given a burial instead of cremation in presence of a magistrate.
Expressing concern over the killing of Sharma, Jammu and Kashmir Oil Tankers Association (JKOTA) yesterday went on an indefinite strike across the state demanding security for drivers of oil tankers in Kashmir Valley and arrest of the killers.