The Magistrates Court in Bulawayo dismissed his bail application on the basis that public security was a consideration and that "what happened in Egypt is a reality." However, Mavhudzi's lawyer, Lizwe Jamela, said they were working on the relevant papers to apply for bail with the High Court.
Mavhudzi, who was arrested in Bulawayo on February 24, was remanded in custody to March 25.
According to prosecutor Jeremiah Mutsindikwa, the 39-year-old had "unlawfully suggested" to Prime Minister Morgan Tsvangirai the taking over or attempt to take over the government by unconstitutional means or usurping the functions of the government.
He had thus allegedly sent an email to the Prime Minister saying: "I am overwhelmed, I don't want to say Mr or PM what happened in Egypt is sending shockwaves to dictators around the world.
"No weapon but unity of purpose worth emulating, hey."
Mavhudzi is the first Zimbabwean to be arrested for allegedly subverting a constitutional government following comments he posted on a Facebook page belonging to Tsvangirai.