"I don't think this bill is going to help protesters achieve their goals. Second, it has an impact on U.S.-China relations. I think this is going to worsen relations," said Max Baucus, who was appointed ambassador by President Barack Obama.
It will also cause more uncertainty regarding potential trade agreement, added Baucus, who is also a former Democratic senator from Montana.
The chamber approved a measure that aims to protect human rights in Hong Kong by a 417-1 margin amid efforts to crack down on months of anti-government protests. The House passed a second bill to bar the export of certain munitions to Hong Kong police by the same margin.
The Senate unanimously approved both pieces of legislation, so they head to Trump's desk after House passage. And Trump will likely sign the bill, Baucus told CNBC's "Squawk Box."
"It sounds good for American politicians. It sounds good for President Trump. (There's a) wonderful top line vision to it: standards for human rights," said Baucus.
"It's very hard in the current political climate in Washington D.C. which has near hysterical reactions against China to not sign the bill of human rights," he added.
Former U.S. Army Lt. Gen. Karl Eikenberry told CNBC on Thursday that the passing of the bill "has infuriated Beijing."
"If we look at the sources and the continuing competition between the United States and China, it is evident to me that ideology political values will play an ever-increasing role," Eikenberry said.
He explained that the conflict between the two countries is that they believe in different ideologies.
"We can look at Hong Kong and step back and put that in a larger context and within the U.S., part of our DNA is the idea of commitment to human rights and to universal freedoms," he said.
Chinese State Councilor and Foreign Minister Wang Yi told former U.S. Defense Secretary William Cohen during a meeting in Beijing that Beijing resolutely opposes the passing of the pro-Hong Kong rights bill, and will never allow anyone to undermine the "one country, two systems" principle, the Chinese foreign ministry said in a statement on Thursday.
The bills come at a tricky time for Trump, who hopes to have a China trade victory to promote on the 2020 campaign trail. Major U.S. stock indexes fell Wednesday after a Reuters report that the world's two largest economies may not finish a "phase one" trade deal this year.
A former U.S. diplomat to Beijing told CNBC on Wednesday, however, he expected a "phase one" deal to get done.
"If there is a phase one trade deal in the offing, it's almost certainly going to be a deal largely on Beijing's terms; something that Beijing will want — purchases and promises, not a deal reckoning on the structural process," said Robert Daly, director of the Wilson Center's Kissinger Institute on China and the United States. "China would want that deal even if it felt insulted over Hong Kong."
But Baucus said China may be rethinking the deal as well.
"Now that President Trump is going through preliminary, if you will, impeachment proceedings, that's causing the Chinese, I think, to back off; they are not sure what's the kind of deal they want to sign with President Trump," said Baucus.
— CNBC's Jacob Pramuk contributed to this report.