The Australian overseas player was hit on the helmet by New Zealand pace bowler Matt Henry towards the end of the Yorkshire innings as the home side scored 180-5 after winning the toss.
But although Marsh was able to continue on his way to an unbeaten 31, he complained of dizziness during fielding practice during the interval between innings and did not return as the visitors won with two balls to spare.
The 34-year-old has been ruled out of tonight’s T20 match against Durham at Chester-le-Street and Sunday’s County Championship game against Essex at Scarborough.
Yorkshire will continue to monitor his condition over the coming days.
Marsh had worked the ball around with typical fluency as Yorkshire raised a competitive score before a crowd of 7,902.
The left-hander added 67 for the fourth wicket in 8.2 overs with debutant overseas signing Sarfaraz Ahmed, who top-scored with 42 from 31 balls with two fours and three sixes.
Adam Lyth chipped in with 34 and Tom Kohler-Cadmore 29, and captain Tim Bresnan hit an unbeaten 16.
But Derbyshire inflicted Yorkshire’s first T20 defeat at Headingley in 11 games dating back to last season in a blow to their hopes of reaching the quarter-finals.
On an evening of watery sunshine that later brought one or two rain flurries, Yorkshire showed two changes to the team that lost to Nottinghamshire on Sunday.
Sarfaraz replaced Peter Handscomb, the overseas player who has now returned to Australia, and Matthew Fisher came in for fellow pace bowler Liam Plunkett, who pulled out after suffering a tweaked hamstring.
Lyth and Kohler-Cadmore gave the Yorkshire innings a good start, adding 44 inside five overs before Kohler-Cadmore skied Ben Cotton to cover.
Kohler-Cadmore played some eye-catching strokes – not least a pulled six into the West Stand off Henry – but, once again, he would have been disappointed not to go on, his score of 29 following innings of 37, 1, 27, 12, 0 and 5 in the tournament to date.
Yorkshire reached 54-1 at the end of the six-over powerplay, a solid platform for a side that have three times passed 220 this season.
But the hosts lost two quick wickets as David Willey fell in similar style to Kohler-Cadmore, skying leg-spinner Imran Tahir to cover, and Sarfaraz came in at 81-3 after Lyth pulled Henry to deep mid-wicket as though giving catching practice, the left-hander having played nicely up to that point.
Sarfaraz got off the mark second ball when he pushed the off-spin of Wayne Madsen to mid-on, but he took a little time to find his rhythm, which was perhaps understandable given that he had batted only twice since the end of May.
Diminutive and busy, Sarfaraz is something of a character and a showman, and several times he reproached himself with word and gesture when he failed to get the ball away as he would have wished, which sometimes happened when he tried to dab through the third-man region.
But Sarfaraz became increasingly fluent and could be pleased with his first contribution, ended when he was bowled by Hardus Viljoen trying that dab shot again through the third-man area.
The other wicket to fall was that of Jack Leaning, who was also bowled by Viljoen.
Bresnan took the first wicket in the Derbyshire reply on 24 in the fourth over when Tom Wood skied to mid-wicket, and the visitors slipped to 46-2 in the sixth when Luis Reece shovelled Steve Patterson to short third-man.
Billy Godleman and Madsen added 77 for the third-wicket in eight overs before Godleman rather gave it away, edging Willey to wicketkeeper Sarfaraz as he tried to guide through third man having made 67 from 48 balls with five fours and three sixes.
Madsen made 47 from 34 balls with four fours and a six, his innings ended when he helped Patterson to mid-wicket.
Two balls later, Patterson picked up his third wicket when Henry was caught at long-on in front of the Football Stand.
It was anyone’s game going into the closing stages, but captain Gary Wilson and Hughes held their nerve, Hughes striking the first ball of the 20th over bowled by Bresnan – from which 10 runs were wanted – for six over long-on to effectively settle the issue.