Consequently, the English and Wales Cricket Board have summoned him to appear before a disciplinary hearing when he returns from a holiday abroad.
The ECB chief executive, Tim Lamb, said: "It is a potentially serious matter but it would be quite wrong of us to pre-empt the result of the disciplinary hearing.
"It is only right to give Phil the opportunity to put his side of the story."
Tufnell, who is in the party for England's winter tour of the West Indies, will be asked for his version of events at the hearing.
A career-best unbeaten 203 from Guy Whittall helped Zimbabwe to 461, their third highest total in 24 Tests, on the second day of the second and final Test in Bulawayo yesterday.
In reply New Zealand were 23 without loss at close of play.
Whittall began the day on 66, having been dropped on 19 on Thursday evening, and went on to record Zimbabwe's third double century and their second highest Test score. Between lunch and tea, he scored 86 of the 103 made in the session.
The 25-year-old right-hander shared stands of 78 with David Houghton (32) and 73 with Heath Streak (17) before frustrating New Zealand further with a 40-run final-wicket stand in 68 minutes with Everton Matambanadzo who made four.
His century came up in four and a half hours and in all he batted for 461 minutes, facing 360 balls, hitting 22 fours and two sixes.
New Zealand's 18-year-old left-arm spinner Daniel Vettori did the bulk of the bowling, sending down 58 overs and finishing with 4 for 165.
Worcestershire yesterday denied reports that the England fast bowler Devon Malcolm would be moving to New Road on a contract worth pounds 70,000- a-year.
The ECB yesterday announced it has secured a major deal with Pepsi-Cola prior to the World Cup in England in 1999. Pepsi will be the main sponsor of the event.Reuse content