The Kano state intelligence chief, Bassey Etang, and a separate military statement described the compound as hosting a "terrorist cell" tied to the powerful Lebanese Shiite movement Hezbollah.
No evidence was provided linking the home to the Lebanese group.
Journalists were brought to the compound in the upmarket Bompai neighbourhood of Kano and taken to a bunker dug beneath a bedroom where weapons had allegedly been stored.
"The weapons include anti tank weapons, rocket propelled guns, anti tank (and) anti personnel mines among other dangerous weapons," the military statement said.
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"This is the handiwork of Hezbollah. What has just been discovered is the cell of Hezbollah and what you have seen here is a Hezbollah armoury," said Etang area director of the Department of State Services, Nigeria's main intelligence branch.
"These weapons are meant to be used to target Israeli and Western interests in Nigeria," he told reporters.
Nigeria is confronting an insurgency waged by radical Islamist group Boko Haram that has left thousands dead since 2009.
Analysts see Boko Haram primarily as a domestic group that has possibly sought closer ties to Al-Qaeda's west Africa franchise.
The military statement said that one suspect, Mustafa Fawaz, was arrested on May 16, and his "confession unveiled other members of the foreign terrorists network."
A second suspect, Abdullah Tahini, was arrested several days later while trying to board a flight to Beirut from the Kano airport, according to the military.
The third detained Lebanese national, Talal Roda, was arrested at the Kano home on May 26 while Fauzi Fawad was identified as the suspect who is at-large.
An employee who answered a call to a number listed for Wonderland told AFP that Fawaz had not been in the office this week.
The arrests and arms recovery followed a "robust counter terrorism investigation...In the past several months," the military said.
Nigeria is home to a sizeable Lebanese population, including in the mainly Muslim north.