Police said the policeman was injured in Kaka Sarai area of Srinagar on Friday. The civilian was injured in Soura area on Saturday.
Clashes erupted in many places in the Kashmir Valley after the congregational Eid prayers on Saturday.
Stone-pelting youths engaged the security forces in pitched battles in Eidgah and Soura areas of Srinagar and in Anantnag, Pulwama, Shopian, Baramulla and Sopore towns on Saturday.
Over two dozen civilians and 11 security personnel were injured in the clashes.