The former England international was diagnosed with a pulmonary embolism after developing respiratory problems following a back operation, the club has confirmed.
Robinson is now at home, having spent the weekend being monitored in hospital, but is likely to miss the start of next season.
|5/1||Blackburn are 5/1 to be relegated with Coral|
Kean requires an operation on his left knee after tearing cartilage during the 3-0 defeat to Cardiff on Monday and will be out for six weeks, leaving Grzegorz Sandomierski as the club's only available keeper.
Rovers are currently 19th in the Championship with six games remaining, level on points with Huddersfield, who occupy the final relegation spot.