About 20 people carried banners outside of courthouse in Lahore, condemning Facebook and praising Prophet Mohammed.
Lawyers also petitioned the Pakistani government to register a strong protest with Facebook’s owners.
"The competition has hurt the sentiments of the Muslims," lawyer Chaudhry Zulfikar Ali said.
Facebook users in Pakistan, however, told AFP they could still access the site after the ban was imposed on Wednesday.
Officials with the Pakistani government told the court they had already blocked Facebook pages relating to the competition, but the lawyers group argued that no part of a site can be banned unless the entire site is blocked.
Pakistan has 45 million Facebook users, according to lawyers.
The Facebook page for "Everybody Draw Mohammed Day" had just over 40,000 supporters while the opposing "Against Everybody Draw Mohammed Day" had more than 53,000.