City said on their website that Jesus had "suffered a medial collateral ligament injury" and will have further examinations this week to establish the extent of his lay-off.
City manager Pep Guardiola said immediately after the match that Jesus would "be out for a little bit more than one month."
The 20-year-old forward left the Selhurst Park pitch in tears after landing awkwardly during the first half and had to be consoled by his club's medical staff.
"Today I went through an image exam on my left knee that diagnosed a small medial collateral ligament injury," Jesus wrote on Instagram on Monday.
"Thank God it is not very bad and I won't have to go through any surgery procedure. Promise to be back as soon as possible."
City are 12 points clear at the top of the table before facing mid-table Watford at home on Tuesday.
(Writing by Ken Ferris; Editing by Greg Stutchbury)
