Cobolli, the 10th seed, was due to be playing in his first Grand Slam semi-final but will instead benefit from some extra rest ahead of Sunday's final.
"It's tough for me to speak also. When he came to me an hour ago, I almost cried," said Cobolli of his friend Arnaldi, as they held a joint press conference while sitting three metres apart.
"I was ready to play this match and when he came I was completely sad for him, but at the same time of course I'm really happy for the result that I reached this week."
World number 104 Arnaldi had spent the most amount of time on court for a player en route to a Grand Slam semi-final, winning marathon matches in the third and fourth rounds.
His quarter-final opponent, Matteo Berrettini, retired injured in the second set of their last-eight tie.
But Arnaldi's dreams of a remarkable Slam title were ended by a virus.
"It's tough, because for how the tournament was, for how many hours I've been on the court, I was feeling actually very good," he said.
"To have to withdraw from the first (Grand Slam) semi-finals is not something that you wish to do anyway, and I tried to get ready and try to stay as much as I could here and try to see if I could go forward.
"But every time I get up I feel dizzy and I don't feel like the best, and I'm pretty sure if I eat again I'm not going to feel good, so that was the right decision."