"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 John Kirwan said.
Blues doctor Stephen Kara, consulting with New Zealand Rugby medical director Dr Ian Murphy, said Weepu was to undergo further tests.
"Piri will be out of rugby for a minimum of four weeks while we continue to investigate this condition."
Thanks for all the support guys, much appreciated. I'm sweet, looking forward to getting back on the park as soon as possible.. #JahBless
Weepu is now undergoing testing to determine the cause of the stroke which appears to have occurred before the team travelled to South Africa in early March.
"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. He had no other symptoms to raise further concern while we were away," Dr Kara said.
"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," Dr Kara added.
"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."
New Zealand Rugby General Manager Neil Sorensen said that the 71-Test cap All Black was being supported by New Zealand Rugby and the Players Association.
"We know that Piri is pretty tough and has proven his ability to bounce back from any medical issue he has had. He has access to the best possible care and support."