The 23-year-old went in on Sunday, 8 January and came out four days later.
Blues said the loose-head "will be closely monitored by hospital doctors and the Cardiff Blues medical team".
Danny Wilson's side are also without loose-head Gethin Jenkins, but Rhys Gill is hoping to be fit to face Bristol on Saturday.
Wilson hopes Wales utility back Gareth Anscombe - who is not in Rob Howley's squad for the 2017 Six Nations - and number eight Nick Williams will be fit for the European Challenge Cup encounter.
In their statement about Thyer, Blues said: "Following advice from the region's medical team, Thyer attended hospital where comprehensive investigations took place.
"He was released from University Hospital of Wales, Cardiff last Thursday (12 Jan) and continues his progress from home.
"There has been regular contact with family and Thyer will be closely monitored by hospital doctors and the Cardiff Blues medical team. Further information will be released in due course."
Cardiff Blues prop Brad Thyer spent four nights in hospital after suffering "delayed" concussion following their 7 January Pro12 loss at Glasgow.