A Zimbabwe Cricket media release confirmed on Wednesday that Panyangara had been "expelled" from the Zimbabwe camp because of "indiscipline", but gave no further details.
"The 28-year-old Panyangara has also been fined one match fee for his behaviour that the national team disciplinary committee found to be disruptive in the build-up to the first ODI of the triangular series, which Zimbabwe played against Australia on Monday," the statement read.
In the video, Johnson is seen taking wickets but also terrorising England's batsmen with short deliveries.
Although the message was intended as a joke to Zimbabwe's batsmen, their coach Stephen Mangongo and chief selector Givemore Makoni failed to see the funny side.
Panyangara took 0 for 68 in seven overs as Zimbabwe lost to Australia by 198 runs on Monday, and will now train with the Zimbabwe A squad that is preparing for a tour of Bangladesh next month.