Emin Hodzic, 25, had already been sentenced last year to a year in prison for having joined the ranks of the Islamic State group in Syria in 2013 for three months.
Last week, he was arrested at Sarajevo's bus station, not far from the US embassy. In the boot of his car, police found a rocket-launcher, two automatic rifles, a large amount of ammunition, an anti-personnel mine, four grenades and two assault vests, according to the prosecution.
"Sarajevo's municipal tribunal ordered the detention of Emin Hodzic for one month," said the spokesman for the regional prosecutor's office, Azra Bavcic.
Hodzic has been charged with illegal possession of weapons and explosives.
The US embassy in Bosnia has been the target of a terrorist attack before.
In October 2011, Mevlid Jasarevic, an extremist, opened fire on the building with an automatic weapon for nearly an hour.