"Ryan has been speaking of the incident yesterday and will continue to be monitored at the hospital over the coming days," Hull said in a statement.
The club said Dawson, club doctor Mark Waller, head of medical Rob Price and club secretary Matt Wild had all visited the player at St Mary's Hospital.
Mason, 25, suffered the head injury in a first half collision with Chelsea's Gary Cahill and was rushed to hospital in London for surgery after being treated for 10 minutes on the field.
Struggling Hull lost the match 2-0 and remain one place above bottom club Sunderland.
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(Reporting by Alan Baldwin, editing by Ed Osmond)
