The bill -- passed late on Thursday but due to be re-approved Friday for technical reasons -- threatens fresh sanctions against Russia and opens the way for the provision of up to $350 million (280 million euros') worth of military hardware to Ukraine, which has been fighting an eight-month war against separatists in its eastern region.
The "Ukraine Freedom Support Act", which must still be approved by the White House, allows for the delivery of anti-tank and anti-armour weapons, radar, surveillance drones and communications equipment to Ukrainian forces.
But Moscow immediately issued a statement through its foreign ministry expressing "deep regret" at the move.
There is little appetite in Western capitals for a move that could see them drawn into a proxy war with Russia and it is far from certain that President Barack Obama will back the Senate's bill.
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Senate lawmakers also pulled a clause at the last minute that would have granted "major non-NATO ally" status to Ukraine, along with Georgia and Moldova.
Russia denies the accusations despite a wealth of evidence.
Meanwhile, Ukrainian President Petro Poroshenko said a ceasefire put in place on Tuesday -- the fourth since the conflict began in April -- was "real" but still remained fragile.
"Today is the first 24 hours for seven months... When we have a real ceasefire in Ukraine," Poroshenko said during a trip to Australia.
"Everything is so fragile. But I pray that we should continue this process.