The trio, all aged in their 30s and from the East Anglia, East Midlands and North West regions of England, are being questioned by detectives, Leicestershire Police said.
It asked people to "resist speculating about the identities of those arrested, the circumstances that may have led to their arrest and the cause of the explosion.
"No further details will be released about these individuals at this stage," the statement added.
The blast in the central English city on Sunday evening demolished a supermarket and a two-storey flat above, killing five people.
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Mary Ragoobeer, 46, and her sons Shane, 18, and Sean, 17, are officially listed as missing but are feared dead.
Shane's girlfriend Leah Beth Reek, 18, and 22-year-old shop worker Viktorija Ijevleva are also unaccounted for.
Human remains were recovered from the rubble, after debris was thrown across four lanes of traffic by force of the explosion.
Formal identification of the remains has yet to be carried out.