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| Ms Geller is an outspoken critic of Islam |
The American Freedom Defense Initiative wanted to display the cartoon, which won first prize at an event in Texas.
Two gunmen were shot dead by police outside the event earlier this month.
Washington transport authorities on Thursday banned political, religious and advocacy adverts on the subway.
The transport authority in the US capital voted unanimously to suspend advertisements it describes as "issue-oriented".
AFDI founder Pamela Geller strongly criticised the decision to ban the advert, describing it as an attack on free[dom] of speech.
Ms Geller commented on her website that "rewarding terror with submission is defeat, absolute and complete defeat. "These cowards may claim that they are making people safer, but I submit to you the opposite. They are making it far more dangerous for Americans everywhere."
The advert calls for Americans to support free speech and features a bearded, turban-wearing Muhammad waving a sword and shouting: "You can't draw me!"
In reply, a cartoon bubble portrays an artist grasping a pencil and saying: "That's why I draw you." » | Friday, May 29, 2015
JIHAD WATCH: Assassin’s veto: Washington Transit Authority shuts down free speech, suspends all issue-related ads » | Robert Spencer | Thursday, May 28, 2015
