Coalition spokesman Brigadier General Ahmed al-Assiri confirmed that the truce had taken effect. The rebel forces have yet to say if they will abide by the ceasefire.
It coincides with the start of United Nations-brokered talks in Switzerland between Yemeni government and rebel representatives.
Shortly after the ceasefire began, mortar rounds hit pro-government forces south of the flashpoint city of Taez, a Yemeni security official said.
"Five mortar rounds hit positions of the legitimate forces in Shuraija after the truce entered into effect," said police officer Taha al-Subhi.
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The coalition said earlier that the truce followed a request by Yemeni President Abedrabbo Mansour Hadi, but warned it "reserves the right to respond in case of any violation" by the rebels.
In May a five-day pause in fighting proposed by Saudi Arabia allowed some aid into Yemen before the coalition resumed air strikes, blaming ceasefire violations by the Iran-backed Huthi rebels.
Under the Hadi government's ceasefire plan, a seven-day truce "would be renewed automatically if the other party commits to it", the coalition statement carried by the Saudi state news agency SPA cited Hadi as saying.