The 30-year-old had a scan on Monday after complaining of migraine-like symptoms dating back to the start of this month, and would need further tests to determine the cause of the stroke.
"Piri and his family have the full support of the organisation. He's getting the best possible care and advice and we are grateful this has been picked up by our medical experts, as often minor strokes remain undetected," Blues head coach Sir John Kirwan said on the team's website (www.theblues.co.nz).
The stroke may have occurred before the team travelled to South Africa in early March, the team said.
"Piri presented with transient symptoms that could have been from a migraine before he travelled and was cleared by specialists to travel, as long as he was monitored," team doctor Stephen Kara said.
"He had no other symptoms to raise further concern while we were away.
"We took the precaution of getting an MRI scan for him this week and we are thankful we are now getting to the bottom of this issue.
"Having spoken to Auckland City Hospital specialists, we are very confident that Piri's condition is not associated with any injury, in particular, any head injury.
"This was a minor stroke and he is expected to make a full recovery. However any stroke is serious for anyone at any age and we must now take the time to fully understand the cause of it and the implications for Piri."
Bryn Hall will start at scrumhalf for the Blues, who lie eighth in the southern hemisphere competition and take on New Zealand rivals, the Highlanders, at Eden Park on Saturday.
Kirwin has also promoted explosive inside centre Ma'a Nonu and fellow All Black Jerome Kaino to the starting side from the bench as the players recover from injuries.
Kaino starts at blindside flanker as Steven Luatua shifts to number eight to cover Peter Saili, who had suffered a sore foot and was unable to take full part in training.