The Wales international missed a last-minute penalty in Saturday's 20-18 loss at the Liberty Stadium and admitted after the match that he was struggling to remember the final stages of the contest.
Ospreys are happy with the tests carried out at the time, however, and say that the fly-half - off the field for nine minutes following a clash of heads - will now abide by fresh return-to-play protocols.
"Having resumed playing, Dan reported no further symptoms and his actions caused no undue concern for the medical team at that time," a club statement read.
"Dan will continue to be monitored as part of the HIA (head injury assessment) protocol in case of any delayed reaction. The medical welfare and well-being of players is the utmost priority of everybody involved at the Ospreys at all times."
Biggar's Ospreys side have now lost three games in a row, but remain third in the Pro12 standings.