The humanitarian pause -- which began at 11:00 pm (2000 GMT) on Tuesday -- is the first break in the air war in support of exiled President Abedrabbo Mansour Hadi since its launch on March 26 and has strong backing from Washington.
Hours after it took effect a Saudi defence ministry official said rockets were fired from Yemen's rebel-held north, hitting the border areas of Jazan and Najran inside the kingdom.
The official said there were no casualties and that Saudi forces had "practised self-restraint as part of their commitment" to the truce.
A US State Department spokesman said that while the truce was "broadly" holding, it had received some reports of clashes after the ceasefire began.
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"We urge all parties to continue to... Honour the commitment to restraint," spokesman Jeff Rathke said.
As aid agencies said they were starting to deliver assistance, residents of the rebel-held capital Sanaa told AFP the ceasefire came as a much-needed relief.
"We hope this truce becomes permanent. We finally managed to sleep peacefully last night," said 25-year-old Mohammed al-Saadi.
The Huthi rebels, allied with army units loyal to ex-president Ali Abdullah Saleh, have taken control of large parts of Yemen including Sanaa and were advancing on Hadi's southern stronghold of Aden when Riyadh launched the air campaign.