The sanctions package -- which also contains measures aimed at Iran and North Korea -- passed 419 to three.
"What has happened goes beyond the realms of common sense," Sergei Ryabkov told state-run TASS news agency.
"The authors and sponsors of this bill are taking a very serious step towards destroying the possibilities for normalising relations with Russia."
The sanctions package -- which also contains measures aimed at Iran and North Korea -- passed 419 to three on Tuesday after weeks of negotiations.
It now heads to the Senate before President Donald Trump will face the tricky choice of whether to veto the legislation, which has been opposed by the White House and considerably constrains his ability to lift the penalties.
If Trump does sign off on the bill then Russia looks likely to retaliate, with Ryabkov insisting Moscow has warned Washington "dozens of times" that any new sanctions would "not go unanswered."
But for now Moscow appears to be keeping its powder dry as it waits to see how Trump reacts.
"We are not giving in to emotions," Ryabkov said.
"We will work to look for ways to move ahead, persistently and consistently searching for ways to compromise of issues important to Russia and the US."
Ties between Russia and the US plummeted to their lowest point since the Cold War after the Kremlin's seizure of Crimea from Ukraine in 2014 saw Washington impose sanctions on Moscow.
Trump repeatedly pledged during his campaign to try to boost relations with Russia, but allegations that the Kremlin meddled in the vote to get him to the White House have made any signs of going soft on Moscow politically toxic.