The Britain-based Syrian Observatory for Human Rights said government and rebel forces were fighting in the Wadi Barada area, where opposition fighters have cut water supplies to the capital.
A resident confirmed the sound of shelling in the area this morning.
Observatory director Rami Abdel Rahman said it was unclear who had started the clashes, with both sides blaming the other.
Syria's government had been shelling the area before the truce began at midnight as it pushes rebels there to accept a "reconciliation deal" and leave the area.
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Opposition figures however say the truce applies to all opposition-held territory, even where Fateh al-Sham is present.
Last week, rebels attacked water infrastructure in Wadi Barada and neighbouring Ain al-Fijeh, cutting supplies to the capital.
Four million people in Damascus and its suburbs have now been without water for a week, the UN says.
The clashes in Wadi Barada were the most serious of several isolated incidents of violence since the truce began.
The Observatory reported early morning clashes in the central province of Hama between the government and jihadist fighters.
The ceasefire is the first nationwide truce to be implemented in the country since September, and is intended to pave the way for new peace talks in Kazakhstan being organised by Russia, Turkey and Iran.
Syria's government hailed it as a "real opportunity" to find a political solution to the war, which has killed more than 310,000 people since it began with anti-regime protests in March 2011.
It was also welcomed by key regime ally Iran as a "major achievement."
And despite being left out of the process, Washington also described the truce as a "positive development".
Sam Heller, fellow at The New Century Foundation, said there was "real interest and urgency" from Moscow and Ankara, but expressed doubts about whether Iran and Syria's government were on board. "All indications are that Iran and the regime want to continue towards a military conclusion.