The Department of State Services (DSS) said two men were arrested in a dawn raid on Friday on suspicion of plotting an attack on the northern city of Kano.
A third man, described as an "explosive expert", was arrested in Kano state on Tuesday, DSS spokesman Tony Oyuipo said in an emailed statement.
"Their plan, together with others now at large, was to assemble the explosives and use them on select targets during the Eid al-Fitr celebrations," he added.
The arrests had "nipped in the bud" potential end-of- Ramadan attacks in Kano, Sokoto, the northern city of Kaduna and Maiduguri, in the northeast, said Oyuipo.
"Terrorist elements" had been plotting "a series of coordinated attacks using explosives on different cities", he added.
Markets, public parks, processions, mosques and Muslim prayer grounds were said to be targets.
Boko Haram was not named in the statement but it has repeatedly attacked similar "soft targets" packed with civilians in the past.
But Boko Haram has continued to mount sporadic raids and suicide bombings, including on June 19, when at least 16 people were killed near a camp for the displaced just outside Maiduguri.
Earlier this month, security sources told AFP the group was planning a surprise attack in Kano on Eid al-Fitr, which is known in Nigeria as Sallah.
In July 2014, Eid festivities were cancelled in Kano after two deadly bomb attacks in the city blamed on Boko Haram.
"This restriction, though regrettable, is necessary in view of recent security concerns," he added.
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