Speaking on CNN's "New Day," the Virginia Democrat told co-host Chris Cuomo that the military action had "no legal justification" considering that the President did not seek approval from lawmakers beforehand.
"There is no legal justification for this," Kaine said. "He should not have done this without coming to Congress."
Trump ordered the launch of 59 Tomahawk missiles
in retaliation for the chemical attack on Syrian civilians, which has been blamed on the government of President Bashar al-Assad.
Although Kaine agreed with several of his colleagues -- specifically, fellow Sen. Marco Rubio -- that "from a moral standpoint ... it was the right thing to do," he said Trump was wrong to not obtain the go-ahead from Congress.
"I'm the Democratic lead on the committee over the Middle East; I was not consulted," said Kaine, who chairs the Senate Foreign Relations Subcommittee on Near Eastern and South and Central Asian Affairs. "I heard about this on the news."
When Cuomo pointed out that "there is a pattern of (Congress) allowing" military actions without obtaining congressional approval, Kaine fired back.
"When you say it doesn't matter, I know you are kind of blasting Congress," Kaine said. "There's 1.6 million families like mine who have a kid in the military. It matters. You can't put people into harm's way without a political consensus."
Later on "New Day," Republican Sen. Cory Gardner said that while he also was not notified of the strike, he believed the military action to be "an appropriate response."
Pointing to the Authorization of the Use of Military Force issued in 2001
used to justify actions against terrorists around the globe, the Colorado lawmaker argued the President "did have the authority to do that."
"I understand that there was the appropriate consultation with members of Congress, and I'm looking forward to more in terms of classified information and a plan coming forward from the administration," said Gardner, who chairs the Senate Foreign Relations Subcommittee on East Asia, the Pacific, and International Cybersecurity Policy.
Should the administration pursue further military action, however, Trump would have "an obligation to come to Congress," Gardner said.
"We have ceded far too much authority," Gardner said. "I do think it is time for Congress to step up into this fight."
"But I don't question the ability or the resolve of this President when it comes to this strike," Gardner added.
House Minority Leader Nancy Pelosi called Friday for the House to return to the Hill and "immediately" debate an Authorization of the Use of Military Force against Syria. In a letter addressed to Speaker Paul Ryan
, the Democrat pointed to the Assad regime's ongoing brutality and urged that "Congress must live up to its Constitutional responsibility."