According to the official SANA news agency on Friday, a security member was also wounded in the exchange of fire.
The clash with members of Jund al-Sham rebel group took place in Khashman area on the outskirts of the city of Hasaka, 700km northeast of Damascus.
A human rights activist in Hasaka, Nidal Darwish, told journalists that "a heavy exchange of fire took place in Khashman quarter, a poor area northeast of Hasakah, led to the killing of one person and wounding two others who were detained".
The incident occurred a week after security forces killed five Jund al-Sham members near the city of Hama about 200km north of Damascus.
Jund al-Sham, which in Arabic means Soldiers of Syria, is a well-known organisation that was set up in Afghanistan by Syrian, Palestinian and Jordanian fighters and has links to Abu Musab al-Zarqawi, the head of al-Qaida in Iraq.
Syrian authorities have been monitoring the group for months and had previously clashed with its members, who were believed to be planning to launch bomb attacks in Damascus.
In June, Syrian security forces raided the hideout of the same group in the town of Daff al-Shouk, south Damascus, killing three people. A policeman was killed and another one was wounded.
Last April, police raided a rebel hide-out hours after a mysterious attack in the Syrian capital's diplomatic quarter that killed four people and targeted a building once occupied by the United Nations.
The group also has claimed responsibility for an October attack on resort hotels in Sinai, Egypt, that killed 34 people, and a March bombing on a theatre in Qatar that killed a British resident.