The pace bowler has been left out of the team for the County Championship match against Hampshire at Headingley.
Plunkett, 30, missed training yesterday and the official club photocall, which was held later than usual this year to allow the club’s England players to return from the West Indies tour.
Plunkett, who was one of six Yorkshire players on the trip, has been banished to the second XI and will play in the three-day friendly against Kent in Canterbury, starting on Tuesday.
In an official statement, Yorkshire first-team coach Jason Gillespie said: “I am very disappointed with Liam.
“He knows that he has crossed the line and he will pay the price of missing out on selection for this game.
“Liam has apologised and we have accepted his apology.
“He is disappointed in himself for letting his team-mates down.
“Hopefully, he will learn from this.
“Players are fully aware that we will not tolerate breaches of ill-discipline.
“Our internal code of conduct is sacrosanct and fundamental to driving us on as a successful club.”
Plunkett has worked hard to resurrect his career since moving to Yorkshire in 2012.
He has become an integral member of the team and his improved performances saw him win back his England place last summer.
But this latest incident is a setback to a man who has made 13 Test appearances, the last of them against India at Lord’s last summer.
Plunkett did not play in the Test series in the Caribbean, but he hopes to feature in the two-Test series against New Zealand, starting on May 21.
Plunkett’s place in the XI today has been taken by Will Rhodes.
Yorkshire won the toss and decided to bat in sunny conditions and they welcomed back three of their England players in the form of Adam Lyth, Jonny Bairstow and Adil Rashid.
Joe Root and Gary Ballance have not been made available, however, having featured in all three Tests in the Caribbean
Lyth pressed his claims for a place in the first Test against New Zealand with a fighting innings, reaching lunch unbeaten on 38, with Yorkshire 83-2 from 30 overs.
Lyth, 27, hopes to make his Test debut against New Zealand at Lord’s on May 21 - an ambition boosted by Jonathan Trott’s retirement from international cricket.
The left-hander did his cause no harm in testing conditions against the Hampshire attack, which caused problems at times against a Yorkshire team whose running between the wickets was somewhat uncertain.
Lyth got off the mark first ball with a neat clip for two off his legs off James Tomlinson, who took the first wicket with the opening ball of the third over when he trapped Alex Lees lbw for one shouldering arms.
It was an uncharacteristic misjudgement by Lees, but Lyth knuckled down alongside Cheteshwar Pujara, the India batsman, whose running between the wickets was nevertheless erratic.
A blow on the helmet from Fidel Edwards, the West Indies pace bowler, might have unsettled Pujara, who appeared to be dropped on 12 when he edged Andre Adams to James Vince in the slips.
Pujara should have been run out by Sean Terry when he pushed a ball from Gareth Berg to point, and he eventually fell with the total on 57, caught at second slip by Sean Ervine off Tomlinson for 18.
With Lyth at lunch is captain Andrew Gale, who is unbeaten on 15.