Ms Carroll, 28, a freelance journalist writing for the paper, was seized in western Baghdad on Saturday on her way to interview a prominent Sunni politician.
Her Iraqi translator was found dead nearby with two gunshots to the head.
"The Monitor joins Jill's colleagues -- Iraqi and foreign -- in the Baghdad press in calling for her immediate and safe release," the paper said in a statement which named Ms Carroll for the first time.
The journalist had been living in Jordan for three years and reporting for American, Jordanian, Italian and other news organisations.
"Jill's ability to help others understand the issues facing all groups in Iraq has been invaluable," said Richard Bergenheim, editor of the paper, according to a CNN report.
"We are urgently seeking information about Miss Carroll and are pursuing every avenue to secure her release," he said.
The Monitor said she was captured in Baghdad's Adil neighbourhood, which is considered one of the city's most dangerous.
Three Iraqi television journalists were recently killed in the district.
The Monitor, which is an independent paper focusing on world news, quotes the journalist's driver as confirming she was kidnapped.
He said gunmen stopped the car, dragged him out and drove off in it.
"It was very obvious this was by design," the driver said, according to reports.
"The whole operation took no more than a quarter of a minute. It was very highly organised. It was a setup, a perfect ambush."
The paper quoted unidentified relatives of Ms Carroll as pleading for her release and asking her captors to "consider the work she has done to reveal the truth about the Iraq war."
No individual or group has claimed responsibility for the abduction.
Ms Carroll is the 31st media worker to have been kidnapped in Iraq since the start of the war in 2003, according to watchdog group Reporters without Borders.
Four Christian peace activists, including a Briton, an American and two Canadians, are being held hostage in Iraq.