It was the sixth time Russia has vetoed a Security Council resolution on Syria since the conflict started in 2011 and the fifth time China has blocked action.
Venezuela also voted against the text - drafted by New Zealand, Egypt and Spain - while Angola abstained. The remaining 11 states voted in favor.
"These kinds of pauses have been used by fighters to reinforce their ammunition and to strengthen their positions and this will only worsen the suffering of civilians," Russian UN Ambassador Vitaly Churkin said of the proposed seven-day truce.
The United Nations says more than 200,000 people might still be trapped in rebel-held areas of Aleppo, which are affected by severe food and aid shortages.
Russia said on December 5 it would start talks with Washington on an opposition withdrawal from Aleppo this week as Russian-backed Syrian forces fought to seize more territory from rebels who are struggling to avoid a major defeat.
Churkin argued that action by the Security Council should be postponed to allow time for those talks.
"That is a made-up alibi," Deputy US Ambassador to the United Nations Michele Sison told the council.