He said the deceased woman has been identified as Nigeena Bano. Further details are awaited, he added.
As per reports, the militants barged inside the house of Bano and opened fire at her. Incidentally, her husband Mohd Yousuf Lone was also killed in a similar manner in 2017.
Jalaludin Bhufanda, the injured person was immediately shifted to a nearby clinic from where he was referred to Srinagar hospital for specialized treatment, police said.
Police said that soon after the incident a joint team of army and SOG launched a hunt to nab the assailants.
The incident comes on a day when Eid al-Fitr is being celebrating across the terror-hit region. Pulwama has the highest number of active militants. The region has seen the maximum number of suicide attacks and explosions, say reports. On February 14 this year, 40 Central Reserved Police Force (CRPF) personnel were killed by a Jaish-e-Mohammed (JeM) suicide bomber who rammed an explosive-laden SUV into a CRPF convoy here.
Meanwhile, clashes erupted between stone-pelting youths and security forces in Srinagar, Sopore, Anantnag and Kupwara towns after Eid prayers. Immediately after the Eid prayers, dozens of youths displayed flags of various militant outfits after which they marched on the road, reported news agency IANS.
On Tuesday, security forces busted a terrorist hideout in Jammu and Kashmir's Poonch district and seized a cache of arms and ammunition on Tuesday.
During a search operation in Lassana forest area, the security personnel seized one Chinese pistol, 19 pistol rounds and 213 rounds of AK-47 rifle, they said.
An FIR was registered in the matter and a probe was underway, the officials said.
The search operation was conducted by police and a team of 16 Rashtriya Rifles, they added.
(With additional information from PTI)