The Hindustan Times reported in Monday's attack the militants managed to ambush an army convoy in the province's Srinagar valley despite high security alert in preparation for Singh's visit Tuesday. The prime minister also was expected to be accompanied by Sonia Gandhi, chairperson of the ruling coalition United Progressive Alliance.
The newspaper said several others were injured in the attack, some seriously.
Kashmir is also claimed by Pakistan and the issue remains the main source of tension between the two countries.
The Hindu newspaper said the heavily-armed militants began firing at the army convoy near Hyderpora on the outskirts of Srinagar and also lobbed grenades before fleeing on motorcycles. The attackers later reportedly abandoned their motorcycles and escaped in cars.
The report, quoting an Indian defense spokesman, said six of those injured were in critical condition.
The Times of India said the militant Hizb-ul-Mujahedin claimed responsibility for the attack. The report said a group spokesman called a news agency in Srinagar to warn of more such attacks.
During their two-day visit to Kashmir, Singh and Gandhi will inaugurate a railroad tunnel and an 800 megawatt power project in Kishtwar.
Condemning the attack, Kashmir Chief Minister Omar Abdullah said: "Such high-profile attacks are aimed at restoring the shattered morale of militants while trying to demoralize the security forces," but that they won't succeed.
Prime Minister Singh said the "cowardly attack" would not deter the Indian security forces, who are engaged in bringing peace and order to the Kashmir Valley, CNN-IBN reported.