The Jamaica Football Federation said it was notified by FIFA that a "member of the Jamaican squad returned an adverse analytical finding on his urine sample" after the June 11 game.
The player and the substance involved were not identified.
"The player has been informed and we await further information from FIFA," the federation said in a statement late Wednesday. "The JFF has taken this matter very seriously and a thorough investigation has already started by the chairman of the JFF Medical Committee."
Last week, Jamaican sprinters Asafa Powell and Sherone Simpson were confirmed to have tested positive for oxilofrine, a banned stimulant, among five cases involving track and field athletes.
The JFF said that FIFA will manage the case. The player is likely to receive a provisional ban during disciplinary proceedings.
In a previous doping case, Peru midfielder Joel Sanchez was provisionally suspended when testing positive for the stimulant methylhexaneamine after a 1-1 draw in Bolivia last October.
FIFA suspended Sanchez from all football for two years in March.
Jamaica lost 2-0 in Honduras and is last in a six-team CONCACAF qualifying group led by the United States.