"For now, we can authoritatively confirm that 46 people were killed in the blasts while 45 people were seriously injured," said Chris Olakpe, the police commissioner in Plateau state.
"The place has been cordoned off. Nobody should go there until we finish sweeping the place tomorrow."
The first blast exploded from within a truck at roughly 3:00 pm (local time), with rescue teams rushing to the city's New Abuja Market, the military said.
"Scores died. Mostly women," Pam Ayuba, spokesman for Plateau state's Governor Jonah Jang, said earlier.
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Boko Haram Islamists are widely believed to have active cells in Jos and have attacked the city before, but the area has not been heavily affected by the extremist uprising.
The group claimed a July 2012 attack at a funeral outside the city that targeted mourners and the security services.
Plateau state, which falls on the dividing line between Nigeria's mainly Christian South and mostly Muslim north, has however seen waves of sectarian violence that has killed thousands over the last decade.
"The fire is still raging. Many shops are consumed by the inferno," he said.
Kingsley Egbo of special military unit deployed in Plateau said rescue workers and the security services were struggling to control the crowd amid the chaos.
The bombings follow two separate attacks on the same bus station in a suburb of the capital, Abuja, on April 14 and May 1, that killed more than 90 people. The first was claimed by Boko Haram.