President Cyril Ramaphosa's office said it was disappointed by the claims and said no evidence has been provided to support them.
The country has maintained claims of neutrality in the invasion of Ukraine.
Mr Brigety said at a media briefing in Pretoria on Thursday that Washington had concerns about the country's stated non-aligned stance on the conflict.
He referred to the docking of a cargo ship in the Simon's Town naval base between 6 and 8 December last year which he was "confident" uploaded weapons and ammunition "as it made its way back to Russia".
The presence of the ship, the Lady R, had seemed curious at the time and raised questions from some local politicians.
"The arming of the Russians is extremely serious, and we do not consider this issue to be resolved," Mr Brigety said, in a damning accusation that seems to have caught South Africa's officials off guard.
In the wake of the allegations, the South African government announced the establishment of an independent inquiry led by a retired judge, a spokesman for the president's office said.
The US has been critical for months about South Africa's continued cosy relationship with Russia.
It also expressed concerns about South Africa's participation in military exercises with Russia and China during the anniversary of the invasion of Ukraine.
The naval exercises took place over 10 days in February and were criticised by opposition figures as an endorsement of the Russian invasion.
The South African authorities denied the war games were provocatively timed to coincide with the one-year anniversary and said the country routinely hosts similar drills with other nations, including France and the US.
South Africa previously abstained from a UN vote condemning the invasion. It also refused to join the US and Europe in imposing sanctions on Russia.
The president asked opposition parties to allow for the process to be completed, adding that "in time we will be able to speak about it".
The US State Department has not yet commented on the claims.
If they are true, they not only weaken South Africa's claim of neutrality, but some may even go as far as saying the country is complicit in the ongoing aggression of Russia in Ukraine.
"If South African bullets are found on Ukraine bodies, that is not a position we would want to be in," one expert in international relations said.
The details around the arms cache are still thin. It is not clear if the weapons would have been acquired from a state-owned arms company, or a weapons company based in South Africa.
But either way, this does not bode well for South Africa's international ties, especially with the US, one of its largest trade allies.
At the heart of the issue for South Africa now, off the back of these claims, will be the impression this could create that the country is not only non-aligned but has in fact chosen to be a "soft ally" to Russia, at a time when some Western countries see Russia as an aggressor guilty of human rights violations.