The latest arrests brings the number of men in custody over the blast to five, after three were detained by police on Wednesday, Leicestershire Police said in a statement.
A supermarket and a two-storey flat above it were demolished in the explosion on Sunday evening, which neighbours reported shook their homes.
Those arrested are all in their 30s and come from the East Midlands area which encompasses Leicester, and East Anglia and the North West of England.
A 46-year-old woman and her two teenage sons were killed in the blast, along with one of their girlfriends, 18, and a 22-year-old woman.
Investigators are still trying to establish the cause of the explosion and officers continue to search through the rubble for clues.
Police have refused to comment on British media reports that the site was used as an illegal alcohol distillery, a possible cause of the explosion.