Godin was substituted in the 49th minute of Tuesday's absorbing 1-1 draw at Barcelona, which sent the Catalans through to the Copa del Rey final 3-2 on aggregate following a second leg that saw three players sent off.
Diego Simeone's side have not lost in six league games ahead of Sunday's visit of Celta, but are set to be without their defensive lynchpin for two weeks, according to local reports.
MEDICAL REPORT @diegogodin underwent an MRI that confirmed his grade I muscle injury to the right thigh.— Atlético de Madrid (@atletienglish) February 9, 2017
Simeone is now down to just two fit centre-backs with Jose Gimenez also sidelined.
Luis Hernandez – Godin's replacement on Tuesday – is expected to stand trial in a domestic abuse case later this month.