The remains, which were discovered on Monday, were sent for tests on Tuesday in an effort to identify the bodies, a Karbala police spokesman said.
The men who claim to have discovered the graves were working on underground sewer lines, CBS' Jennifer Donelan reports.
Police will not say how many bodies were found.
Ayad Mashaalah, a local restaurant owner, said he saw bags filled with decomposed bones and corpses.
Mashaalah said human rights workers came and took the bags, which are thought to date back to 1991.
BBC estimates that as many as 30,000 people could have been killed and buried in mass graves during the particular Shiite uprising thought to be the source of Monday's finding.
The apparent discovery came amidst ain Iraq, with at least two dozen people — including two U.S. soldiers — killed in shootings and bombings Monday and 18 on Sunday.
Karbala is a Muslim holy city, site to a biannual Shiite pilgrimage that marks the death of the prophet Muhammad's grandson more than 1,000 years ago.
Human rights organizations estimate that more than 300,000 people, mainly Kurds and Shiite Muslims, were killed and buried in mass graves during Saddam Hussein's 23-year rule, which ended when U.S.-led forces toppled his regime in April 2003.