Both players missed the ongoing Mumbai Test owing to injuries.
Shami had been troubled by an injury on his right leg through the series. The pacer managed to play the first three Tests despite clutching his hamstring while bowling in the opening game in Rajkot.
"BCCI medical team confirms that Indian pacer Mohammed Shami and wicket-keeper Wriddhiman Saha are ruled out of the fifth Test of the Paytm Test Series-2016 starting on December 16, 2016, against England in Chennai," Board of Control for Cricket in India secretary Ajay Shirke said in a statement.
"Shami has soreness in his right knee and has been advised rest and rehabilitation. He will be going to the National Cricket Academy, Bengaluru to start his recovery programme.
"Saha who suffered a hamstring tendon injury in the second Test of the ongoing series against England at Vizag (Visakhapatnam), is undergoing rehabilitation programme at the NCA."
In Saha's absence, Parthiv Patel has taken over the keeping gloves since the third Test in Mohali.
Image: India fast bowler Mohammed Shami
Photograph: BCCI