Fish fell on a slippery surface and got treatment on his ankle before deciding to stop.
"It's just unfortunate," Roddick said. "You know, for a number of reasons. Obviously, Mardy is a friend. I don't want him to be hurt."
Roddick, the defending champion, struggled to gain the upper hand and faced two break points at 2-2 before holding his serve. Fish, who in March defeated Roger Federer to reach the final at Indian Wells, Calif., held off three break points in the next game, hitting two aces and a forehand winner before holding with his seventh ace.
A single mini-break for 2-0 in the tiebreak was enough for Roddick to win the set.
"I want to see him be OK," Roddick said. "Next week might be a question, but hopefully [he'll be OK] for Wimbledon."
Roddick returned to competition after missing several weeks with a shoulder injury, so the shortened match was appreciated.
"Me coming off of an injury, you know, we were out there for about an hour, so that's about right for me," Roddick said. "I hit it pretty well yesterday and today. So it's pulling up all right."
French Open champion Nadal needed three sets to defeat Japanese teen Kei Nishikori, winning 6-4, 3-6, 6-3.
"Yeah, tough match," Nadal said. "He played well. I didn't play my best match, but I fight, no? I tried my best all the match. I served well, I think. Was my best shot today. Probably in the third set I start returning a little bit better, no?"
Second-seeded Djokovic rallied to overcome fellow Serb Janko Tipserevic 2-6, 6-1, 6-4 after losing the opening four games.
Roddick next will play Andy Murray, who survived two injury scares before overcoming Latvia's Ernests Gulbis 5-7, 6-1, 6-4. The sixth-seeded Murray double-faulted to concede his serve at 5-5 and then received treatment to his right thumb after Gulbis served out the first set.
After rallying to win the second set convincingly, Murray slipped and injured his groin during the opening game of the third before going on to break for 5-4.
Murray's thumb injury was diagnosed as a sprain and he said he was not sure whether he could play on Friday.
"I'm pretty concerned about it right now," Murray said. "I'll wait and see what it's like when I get up in the morning. When it's something like that, a sprain, it tends to be worse the next day."
Ivo Karlovic, who lost to Roddick in the 2005 Queen's final, upset 10th-seeded Fernando Gonzalez 6-3, 7-5. Four-time champion Lleyton Hewitt defeated Paul-Henri Mathieu 6-4, 6-4, and fifth-seeded Richard Gasquet defeated Mario Ancic 7-6 (5), 6-4.