Bancroft, whose 10-match Test career was marked by his nine-month ban for the ball-tampering scandal in the 2018 series with South Africa, had blood streaming from his nose but was able to walk off the pitch.
Sams, who has played 10 T20 international for Australia, was stretchered off after he and fellow 32-year-old Bancroft had a clash of heads when going for a catch.
"Both players are conscious and talking, demonstrating symptoms of concussion and have possible fractures," Thunder said on X.
"Both have been transported to hospital for assessment."