Fahim, 56, died of natural causes today.
In his message the Prime Minister said that it is with great sadness that he learnt of the passing away of Marshal Fahim.
"He was a brave and fearless military commander, whose contribution to Afghanistan's stabilisation and reconstruction after over three decades of war and conflict will always be remembered," he said.
Singh said that Marshal Fahim was also a close friend of India and the country shall never forget his personal contribution to nurturing and strengthening the India Afghanistan strategic partnership.
"We pray to the Almighty to give the family of Marshal Fahim the strength and fortitude to bear their loss at this time of great sorrow," Singh said in his message.
In a separate message, Vice President M Hamid Ansari said that he was deeply saddened to learn of the passing away of Fahim.
Ansari described him as a fearless commander, one of the bravest sons of Afghanistan, "my friend who devoted his entire life to combating the dark forces of extremism and terrorism that continue to threaten Afghanistan and its people.
"The people of India shall always remember Marshal Fahim for his tireless efforts to strengthen the India-Afghanistan strategic partnership.
"Today our prayers and thoughts are with the bereaved family and the friendly people of Afghanistan. May the Almighty give them strength and courage to bear their loss."