The world number two was serving in the third game of the match when the bees descended upon him. The 20-year-old tried swatting them away with his racket but eventually ran for cover after being stung.
Alcaraz, who emerged with a 6-3, 6-1 victory to keep his title defence on track, said the bees were all over him.
"I saw some bees around but I thought it was just a few of them, just not too many," he told reporters.
"But I saw the sky and there was thousands flying, stuck in my hair, going to me. It was crazy. I tried to stay away from them, but it was impossible."
Play resumed after an hour and 48 minutes, during which a beekeeper was called to control the situation.
"When we stepped on court, there were a few bees in the corner, it was bothering us. We couldn't start playing again. When we decided to warm up a bit to see how it goes, I was hitting some balls and seeing some bees around me," Alcaraz said.
"I couldn't stay focused on the ball, I was focused on the bees and tried to (keep them) away. That's why we stopped a few more times before the match began again.
"After that, we decided to warm up and I saw that the bees weren't around anymore. I tried not to think about them anymore.
"It was a really important game for me. I surprised myself that I stayed focus on the match, not on the bees."
American Coco Gauff, who was also in action late in the day, said she was relieved to avoid the invasion.
"That's the craziest thing I've ever seen happen at a tennis court," Gauff said.
"Hopefully it will never happen again, at least not to me."
