The Brazilian hurt himself when conceding a penalty during City's 1-1 draw at Liverpool on Sunday.
Ederson stayed on the field for the resulting spot-kick, which Alexis Mac Allister scored to cancel out John Stones' opener, but needed to be substituted soon after by Stefan Ortega.
Arsenal lead the Premier League on goal difference from Liverpool with third-place City just one point behind.
The Gunners travel to the Etihad on March 31st.
Ederson is also set to miss Saturday's FA Cup quarter-final at home to Newcastle and Brazil's upcoming international friendlies against England and Spain.
"(It) was my time with Eddie’s injury. I was ready like always," said Ortega.
"It was a special moment to come on in this big game and the whole world watching. It was a nice feeling.
"I enjoyed every second. It’s nothing new what came - I was ready and prepared."
