In the 15.3 overs that were bowled, the hosts progressed from their overnight second-innings score of 20-0 to 62-1.
Cameron Bancroft (22) was the only wicket to fall, edging a John Hastings delivery to Ross Whiteley at slip.
But the bad weather saw an early lunch taken at 12:30 BST at Cheltenham and no further play was possible.
Gloucestershire lead Worcestershire, who are second in the table and started the match 26 points behind leaders Nottinghamshire, by 145 runs going into the final day.
Only 70 minutes of play were possible on day three of the Division Two game between Gloucestershire and Worcestershire because of rain.