The broadcaster said the presenter's outburst towards the Tory MP on Wednesday had breached its "strict" code of conduct.
Guru-Murthy later apologised to Baker and described his behaviour as "beneath the standards I set myself".
A statement from the broadcaster said: "Channel 4 has a strict code of conduct for all its employees, including its programming teams and on-air presenters, and takes any breaches seriously.
"Following an off-air incident, Channel 4 News anchor Krishnan Guru-Murthy has been taken off air for a week."
Guru-Murthy will not now return to Channel 4 News before November 4, due to a pre-existing week of leave.
During an off-air moment after his exchange with Baker, Guru-Murthy was heard to say: "What a c***."
He later tweeted: "After a robust interview with Steve Baker MP I used a very offensive word in an unguarded moment off air.
"While it was not broadcast that word in any context is beneath the standards I set myself and I apologise unreservedly.
"I have reached out to Steve Baker to say sorry."
In an interview with Times Radio, Baker said that sacking Guru-Murthy would be a "service to the public" if he was found to be in breach of his code of conduct.
"I had an interview earlier with a journalist I don't have a great deal of regard for who I felt was misrepresenting the situation through the construction of his question, which I called out, I think live on air, or I thought it was a pre-record," he said.
"And he clearly didn't like that, quite right, too. But I'd be quite honest, I spent a long time live on air, calling him out on his conduct as a journalist and glad to do so any time.
"But it's most unfortunate that he's sworn on air like that. If it's in breach of his code of conduct, I do hope they sack him - it would be a service to the public."
Baker later replied to Guru-Murthy's tweet, accepting the apology and saying he "appreciated" the gesture.