The opposition-aligned group said the five were hit during a demonstration by high school pupils in the main city in Sudan's North Kordofan state. Snipers from the paramilitary Rapid Support Forces (RSF) targetted the children, the doctors' group claimed.
Many others were injured, added the Central Committee of Sudanese Doctors - one of a group of unions and professional bodies that helped lead months of protests against Sudan's long-term leader Omar al-Bashir.
There was no immediate statement from the state security services, or from Sudan's military leaders who ousted Bashir in a coup in April as the protests mounted.
Videos circulating on social media purported to show pupils protesting outside El-Obeid's main hospital against the attacks on protesters. Immediately after the shooting, they started chanting against the military council.
Hundreds of teenagers in uniform chanted "blood for blood, we will not accept blood money" in the footage. The doctors' group did not give details on what first started the protest in El-Obeid, around 400 km (250 miles) southwest of the capital Khartoum.
The acting governor of North Kordofan, Mohamed Khidr Mohamed Hamid, told Al-Arabiya TV there had been a "slight friction" between protesters and security forces. He said he could not confirm who opened fire and a committee would investigate.
The main opposition group Forces of Freedom and Change (FFC) called for Monday's attackers in El-Obeid to be held accountable and for the ruling military council to immediately agree on the details for a new transitional authority.
"Forces belonging to the army and Rapid Support (paramilitary force) indiscriminately and violently fired this afternoon at peaceful demonstrations of secondary school students in El-Obeid," the coalition said in a statement. "Only a civilian authority is capable of carrying out independent investigations into all crimes."
Since the protests started against Omar al-Bashir in December 2018, at least 250 people have been killed in Sudan.
Opposition activists have kept up their demonstrations since April when the president was ousted, pressing for the military to speed up the move to civilian rule and calling for justice for people killed by the RSF during a raid on a sit-in protest in Khartoum in June.
The FFC coalition is negotiating with the ruling military council to finalize an agreement for a three-year transition to elections.
The two sides signed a deal on July 17 setting out the transition's institutions. But talks have been repeatedly delayed since then amid disagreements of the wording of a constitutional declaration to determine the role of a new council to run Sudan.
The latest attack on protesters was blamed on RSF as the military council deputy leader and RSF commander Mohammed Hamdan Dagolo visited Cairo Monday to meet Egyptian President Abdel Fattah el-Sisi.
Egypt, along with the United Arab Emirate, and Saudi Arabia, has shown support for Sudan’s military council which is being rejected by Sudanese protesters, warning that it is taking the country into the direction of a military dictatorship.