The vandal also spray-painted an anarchy symbol, "Murderers" and "Alex was here" on the front of the building. The graffiti was an apparent reference to 15-year-old Alexandros Grigoropoulos, whose recent killing by Athens police has ignited angry protests there.
The cyclist was last seen fleeing southbound on Park Avenue, police said. No injuries were reported.
Police were studying security video for more clues.
The consulate was closed as a precaution on Wednesday amid a New York Police Department investigation, said spokeswoman Polyxeni Mastroperrou. She said no one was inside the location at the time of the incident.
NYPD spokesman Paul Browne said detectives were looking for possible links to the three other unsolved attacks. They suspect one person could have been "trying to make a political statement in all four," he said.
The Times Square incident occurred in March, when a hooded man on a bicycle rode up to the center just before dawn and set off a small explosive that shattered the front door but caused no injuries.
Investigators later recovered a 10-speed bike they suspect was used in the Times Square attack, but no arrests were made.
Last October, two small explosive devices were tossed over a fence at the Mexican Consulate, shattering windows. A nearly identical blast occurred at the British consulate in May 2005.
Witnesses and security video revealed that in both those instances, a cyclist had thrown the devices before pedaling away.
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