The police fired when the protestors attacked the residence of the inspector general of police and that of Haryana Finance Minister Abhimanyu in Rohtak, police officials said.
Life continued to be affected in most parts of Rohtak, Jhajjar and some other districts of the state as the agitation by Jats continued for the sixth day on Friday.
The Jat protestors, who have been demanding reservation in jobs and educational institutions, torched several police and private vehicles in Rohtak. The protestors also damaged private property, and even manhandled media persons at some places in the town.
Haryana Chief Minister Manohar Lal Khattar's officer on special duty Jawahar Yadav dubbed the firing incident as "unfortunate".
BJP leader Anil Jain confirmed the death of one person in police firing.
The injured were rushed to the Post Graduate Institute of Medical Sciences in Rohtak, police said.
The protestors agitating for the past six days have blocked roads, highways and railway tracks in Rohtak, Jhajjar, Sonipat, Bhiwani, Jind, Hisar and some other districts, inconveniencing the common man.
The Jat stir escalated even as the Haryana government called an all-party meeting in Chandigarh to discuss the reservation issue and the Jat protests. The meeting urged the protestors to end their agitation and remove the blockades.
Jat leaders rejected the appeal to withdraw their agitation.
After the all-party meeting in Chandigarh, Khattar said: "The government is in favour of reservation for Jats in the state and is trying to find out ways and means for the same."
Khattar said the government will prepare a draft bill on reservation and seek suggestions in this regard. "The government has positive approach on this demand," Khattar said.
Referring to statements of BJP's Kurukshetra MP Raj Kumar Saini, who is opposed to reservation for Jats, Khattar said Saini had been asked to withdraw his statement against the protestors.
"If the words of Saini have hurt the sentiments of the Jats, all his statements may be treated as withdrawn. Saini was out of station and as and when he comes back, he would take his words back," Khattar said.
The chief minister warned that no one would be allowed to take the law in his hands.
Haryana Agriculture Minister O.P. Dhankar said in Gurgaon that the state government was ready to give special backward class quota to the Jats in Haryana.
With the Jat agitation spreading in Haryana, authorities blocked Internet services in the affected districts.
Internet services, including 2G and 3G, in the worst affected districts of Rohtak, Sonipat and Jhajjar have been withdrawn since midnight, officials said on Friday.
"It has been done to prevent spread of rumours, as this could lead to the situation getting out of hand," a senior Haryana Police official told IANS.
Jat protestors clashed with security forces in Rohtak on Thursday evening when the police tried to remove the blockades. The protestors attacked police with stones and bricks. A police vehicle was damaged in the clash.
"Some roads are blocked by the protestors. We are trying to persuade them to remove the blockades. We have requisitioned paramilitary forces. We are prepared to tackle the situation," Rohtak police chief Saurabh Singh told the media.