The teacher at Batley Grammar School in West Yorkshire, England has gone into hiding after showing the image to pupils during class.
Tabar, 22, rose to viral fame after Instagram posts showed her looking like a ghoulish version of Hollywood actress Angelina Jolie.
"In Russian legal terms even satire can be treated as propaganda," said Mikhail Bogdanov, director of "Deadplay" publisher Komilfo.
Pakistani Christian Asia Bibi has left her home country, in which she was detained since 2009 for allegedly insulting the Prophet Muhammad.
Bibi had been accused of insulting Islam during an argument with neighbors in 2009.
"The police said LGBT individuals are not a social group, and for that reason you can't stoke hatred against them," said Anna Plyusnina, a lawyer with an LGBT Resource Center in the country.
The church still has the option of pursuing a civil case against the filmmakers.
The Christian governor Ahok has been jailed for two years on the "flimsiest of charges," writes historian Carool Kersten.
In Christian-majority New Zealand, even religious leaders believe the law should go
In Indonesia's capital, an estimated 1,000 people showed their support for the Christian Ahok, who has been sentenced to two years in prison.
The governor lost his bid for re-election in an April run-off to a Muslim rival and will hand over power in October.
Pakistan blocked Facebook in 2010 after a social media competition to draw Mohammad went viral.
Blasphemy is a criminal offense in Pakistan that can carry the death penalty.
Mumtaz Qadri killed Salman Taseer in 2011 for criticizing Pakistan's strict blasphemy laws.
The incumbent governor is currently on trial for insulting the Koran.
It's only the fourth blasphemy case in Danish history.
Hikmet Cetinkaya and Ceyda Karan published a cover image from "Charlie Hebdo" magazine.
Expect offense if you mock something sacred, the pope said.
Asia Bibi was sentenced to death in 2010 for blasphemy. Four years later, she's taking her case to Pakistan's Supreme Court