In a statement, authorities say all residents of the two buildings are required to stay home and undergo coronavirus tests overnight.
Those with negative test results will be allowed to leave the buildings at around 7 or 7:30am on Tuesday morning.
Officials say the lockdowns were ordered after untraceable, preliminary positive cases were detected at the buildings.
“The government hopes this temporary inconvenience will completely cut the local transmission chains and ease residents’ worries and fear, so that they will regain confidence in resuming social and business activities in the area, and return to a normal life,” the statement read.
Hong Kong reported 12 confirmed infections on Monday, only one of which was locally acquired.
There were also fewer than 10 preliminary positive cases.