Hoda El-Sadda, a senior member of the 50-member panel, told AFP she and nine others had "suspended work after the arrest of protesters".
As a result, the panel suspended its work for the day, but adjourned its session for tomorrow morning, television reports said.
Egyptian police arrested about 30 protesters among dozens demonstrating in Cairo against an article in the revised basic law that allows the military to try civilians in certain cases, a security official said.
Today, protesters were demonstrating in front of the Shura Council, where the constitution panel sits, when police used water cannon to disperse them and later made arrests.
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"What is happening is threatening the future of our country because this committee of 50 faces risk of exploding. This committee is the cornerstone of the road map," Youssef said on state television, referring to the transitional plan outlined by Egypt's interim rulers after they came to power following the overthrow of Islamist president Mohamed Morsi.
The road map envisages that a new constitution, a new parliament and a new president should be in place by the summer of 2014.
"This won't stop the protest", said Alaa Abdel Fattah, a prominent activist and brother of Seif.
"They used water cannon and then started beating and arresting people," he told AFP.