The first blast took place at the Daher al-Jabal area in Swiada, Xinhua news agency reported on Friday.
The second explosion was caused by a booby-trapped car that went off near the National Hospital of Swaida.
Meanwhile, Sheikh Hammoud Hinnawi, one of the most prominent Druze Sheikhs in Swaida, told Xinhua that the Daher al-Jabal blast was caused by an explosive device that tore through the car of Sheikh Wahid al-Balous, a Druze spiritual leader and outspoken critic of the Syrian regime.
The Syrian Observatory for Human Rights and other activists said al-Balous, who is also a critic of the Islamist militia groups, was killed along with Sheikh, Fadi Naim.
Al-Balous enjoyed a rising popularity in Swaida recently despite his outspoken criticism of the Syrian regime.
Sheikh Youssef Jarbu, a top Druze cleric, told the pro-government "Sham FM" radio that the aim of the blasts is to frame the Syrian authorities and create a gap between the people of Swaida and the Syrian government.
The radio said a state of "cautious calm" prevailed the city after the explosions, denying reports that some armed men in Swaida started storming government institutions and security forces' positions.
The Syrian cabinet condemned the blasts, saying it will not dissuade the Syrian people from continuing to defend their homeland alongside the Syrian army.