FIFA said the incidents were a violation of its regulations, according to the statement.
"It is regrettable that despite continuous pleas for fans to behave themselves, it appears that the behaviour of a small minority of fans has placed the HKFA in this potentially damaging situation," it added.
HKFA said it had been asked to submit information to FIFA by September 22.
Hong Kong fans' anger against China was stoked in June when a promotional poster used by the China Football Association described the city's team as "black skinned, white skinned and yellow skinned".
FIFA had already given a warning to the HKFA after the Chinese anthem was booed at two home games earlier this year.
"We had repeatedly told fans to not jeer the national anthem, but they still did it," HKFA chairman Brian Leung told reporters Friday.
"Everything right now depends on FIFA's disciplinary committee."
The HKFA has sought to play down the jeering at the Qatar match and said last week it would be "disappointed" if FIFA issued a punishment.
Possible FIFA sanctions could include having to play the next home qualifier, which would be against China in November, behind closed doors.
Hong Kong's next qualifying game is away to Bhutan in October before the rematch with China. The two sides played out a 0-0 draw in Shenzhen just across the border from Hong Kong, last week.
The second round of Asian qualifying for Russia 2018 finishes in March and features 39 teams. It also doubles up as qualifying for the 2019 Asian Cup in the United Arab Emirates.
- AAP