Police said the Mimosa did not register with authorities and ignored attempts to make contact, and was headed for Abbot Point Coal Terminal near the town of Bowen in Queensland.
"Federal agents... executed a search warrant on the vessel yesterday at Bowen, Queensland," a police statement released on Sunday said.
"Navigational equipment and charts were seized and the three men were arrested."
The ship's owners were not named.
|Authorities said stricter rules will stop ships from cutting through the marine park [EPA]
Just days earlier another bulk carrier, the Shen Neng 1, ran aground with over 70,000 tonnes of coal in the same marine park off the northeastern state of Queensland.
Australia vowed a major overhaul of shipping regulations after the Shen Neng 1 incident led to claims that vessels were using the reef as a short-cut.
The Shen Neng 1 strayed off-course and crashed into a shoal at full speed last week, leaking tonnes of oil and sparking fears of an environmental disaster at the World Heritage-listed marine park.
Emergency teams are now engaged in the delicate task of pumping nearly 1,000 tonnes of heavy fuel oil from the stricken, 230-meter carrier, which is not expected to be refloated and towed away for several days.