The 24-year-old Odesnik was stopped by customs officers on Jan. 2 as he arrived in Australia for the Brisbane International and Australian Open, and eight vials, each containing 6 milligrams of the performance-enhancing substance, were found in his baggage.
Odesnik, pleaded guilty in the Brisbane Magistrates Court to importing the hormone, the Australian Customs Service said in a statement late Friday. He was fined 8,000 Australian dollars ($7,280) plus A$1,142.80 (US$1,040) in court costs.
"We are extremely disappointed in the behavior of this individual, which is in no way representative of the sport of tennis," the ATP said in a statement e-mailed to The Associated Press.
ATP spokeswoman Kate Gordon wrote that she couldn't comment on any details of the case because it's considered a "current investigation."
Tennis Australia declined comment on Friday, referring questions about Odesnik to the International Tennis Federation. The ITF said it had received notification that Odesnik had pleaded guilty to possession of HGH.
"The case has been referred to the tennis anti-doping program, and we don't have any further comment," the ITF said in a statement to the AP. "It's just like any other case that gets referred to the anti-doping program, we don't have a comment on it."
Under the World Anti-Doping Code _ to which the ITF is a signatory _ Odesnik faces a possible two-year suspension for possession of a prohibited substance.
Odesnik spends part of the year training in Miami. He's coached there by former top-10 player Guillermo Canas of Argentina, who served a 15-month ban in 2005-06 after failing a doping test.
Canas, who coincidentally announced his retirement as a player on Friday, said he doesn't travel with Odesnik and was surprised to hear about the HGH case.
Odesnik ranked 98th, reached the quarterfinals at the Brisbane International and the second round of the Australian Open. He has since played in four tournaments in the U.S., advancing beyond the first round just once.
He turned pro in 2004 and is something of a journeyman, with a 32-42 career record in tour-level matches. He has reached one ATP final, on clay at Houston last year.
The Australian Sports Anti-Doping Authority was aware of the charges against Odesnik.
"ASADA is aware of the matter announced by the Australian Customs and Border Protection Service," ASADA said in a statement. "Under its legislation, ASADA has power to receive information from Customs and to carry out investigations into possible violations of anti-doping rules.
"Under its legislation, ASADA is unable to provide further comment at this time."
Marion Grant, a spokeswoman for the Customs Service's Border Protection Enforcement, said: "This prosecution ... should act as an important deterrent for other elite athletes who are considering similar activities."
Australia's Customs Act has an extensive list of performance-enhancing substances subject to import control.