A statement said the rebels had breached it more than 40 times along the border with Saudi Arabia.
The UN-brokered truce, meant to last three days, began on Wednesday just before midnight.
Rebels, meanwhile, said an air strike on their territory had killed three civilians.
The UN had hoped that the truce might be extended and lead to renewed peace talks.
Rockets were fired by Houthi rebels at Jazan and Najran in Saudi Arabia, the coalition said in a statement.
"Forty-three violations were committed along the border... in which snipers and various weapons were used, including missiles," it said.
The Houthis said a coalition air strike on Thursday killed three civilians in northern Saada province. They also said they had launched attacks across the border on Saudi military camps over the past two days.
The war has killed nearly 7,000 people, mostly civilians, the UN says.
The coalition, which backs Yemen's exiled president, has been fighting the rebels and their allies since March 2015, when a Saudi-led air campaign began.
Five previous ceasefires have broken down within a short time.
The announcement of the ceasefire followed an international outcry over the deaths of 140 people in a Saudi air strike that hit a funeral gathering in Sanaa.
Saudi officials said they had targeted the wrong site by mistake due to "bad information".
The conflict and a blockade imposed by the Saudi-led coalition have triggered a humanitarian disaster, leaving millions of people homeless and hungry and 80% of the population in need of aid.
The Saudi-led military coalition backing the government in the war in Yemen has accused Houthi rebels of repeatedly violating a ceasefire.