The presenter, who joined the programme in February, was told of the decision after Thursday's programme, and was asked not to turn up for work on Friday.
Tonkinson's co-hosts Amanda Byram and Donna Air hosted Friday's programme, along with stand-in Mike McLean.
The show's ratings have been steadily declining for some time, and have fallen further since Johnny Vaughan and Denise Van Outen left the programme in January.
Unofficial figures show just 300,000 people saw Tonkinson's last show on Thursday.
At 0800 BST it was being beaten by Channel 5 children's programme Bear In The Big Blue House, which had 400,000 viewers, and a repeat of Blue Peter on BBC Two, which had 900,000 viewers.
'Moyles approach'
Producers have reportedly approached BBC Radio 1 afternoon DJ Chris Moyles to take over in an attempt to turn around the figures.
A statement from Planet 24, which makes the programme for Channel 4, said: "Paul Tonkinson has been released from his contract as co-presenter of The Big Breakfast.
"The Big Breakfast will continue with its team of regular presenters, who will be joined by a number of guest presenters over the coming weeks."
Stand-up comedian Tonkinson rose to fame on MTV and on BBC Two's The Sunday Show. He was seen by many critics as the best of the show's three presenters.
This week's events will cast further doubt on the future of the morning programme, which has struggled to match its early 90s hey-day, when the programme was hosted by Chris Evans and Gaby Roslin.