The resolution ultimately passed in a party line vote, 23-15.
The censure vote, if passed by Congress, will remove Koskinen's government pension and other federal benefits, but does not formally punish him otherwise. Censure is used by Congress as a tool to publicly reprimand and urge further action -- the vote simply makes a political point.
So far, there is no full House vote scheduled on the committee's resolution.
This resolution comes alongside a separate effort from the House Judiciary Committee, which is expected to discuss a resolution to impeach the IRS commissioner in a June 22 hearing.
"The Resolution expresses the sense of the House that Mr. Koskinen engaged in a pattern of conduct inconsistent with the trust and confidence placed in him as an officer of the United States, urges Mr. Koskinen's resignation or removal, and requires forfeiture of his government pension and any other federal benefits for which he is eligible," the Oversight committee Republicans wrote in a statement.
Critics said Koskinen allowed backup tapes containing potentially 24,000 emails to be destroyed while failing to inform Congress of the destruction of the tapes in a timely manner.
Republicans argued that he gave false testimony before Congress regarding the backup tapes and refused to correct the record when given the opportunity.
The emails involved Lois Lerner, the IRS official at the center of the allegations that the agency targeted conservative groups. The Justice Department in October closed its two-year investigation into the case, declining to bring charges against anyone at the agency.
Rep. Jim Jordan, R-Ohio and chairman of the House Freedom Caucus, an influential conservative group, called the censure vote a "good step," but urged Congress to go further and impeach Koskinen.
"We must truly hold him accountable for his breach of duties related to the IRS targeting of Americans' First Amendment rights. Congress must impeach Mr. Koskinen -- the American people deserve nothing less," Jordan wrote in a statement.
Ranking Democratic Rep. Elijah Cummings called the resolution "a waste of time." The Justice Department closed its two-year IRS investigation in October 2015, with no charges against former IRS official Lois Lerner or anyone else at the agency.
"There was no politically motivated targeting at the IRS. There was no lying to Congress. There was no obstruction of justice. It simply did not happen. After three years and more than $20 million, it is finally time to put these baseless conspiracy theories to rest," Cummings said.