Rice was complaining of muscle tightness, while Gabriel felt some discomfort in his knee.
Both players were duly taken off in the closing stages of Arsenal’s match against Crystal Palace on Saturday, which they won 5-0.
“He (Rice) was feeling some tightness,” said Mikel Arteta. “I don’t know what muscle it was. But when he says that at 3-0 then obviously we don’t want to take any risks.
“The same with big Gabi. He had some discomfort from a tackle in the first-half and he was struggling a bit, so it was the right moment to take him off the field.”
After three defeats on the spin, Arsenal got back on track with a win over Palace that saw them move up to third in the League.
Gabriel opened the scoring from a corner and a Dean Henderson own-goal led to them doubling their lead from another set-piece.
“The reality is that we trained set pieces less in the last week than other aspects of the game,” said Arteta. “This is the beauty of it.
“But we worked on a lot of things that actually happened and we trained them a lot.
“Really pleased with the clean sheet first, which is something that we’ve been lacking to win games with the amount of goals scores.
“And sharing the goals as well which I think is going to make a big impact on the team.”
Leandro Trossard put Arsenal 3-0 up early in the second-half and the win was wrapped up late on by Gabriel Martinelli.
The winger, who started on the bench after struggling with a fitness issue earlier this week, scored twice in the closing stages.
“I think that is going to make him very good,” said Arteta.
“Sometimes when you are in that period and, as well, he had a little issue the last few days in training. He wasn’t fully, fully fit. That changes the momentum and the perception. It re-energises you and I think it’s a good do thing.”