The fake report on Al-Watan was picked up by a number of Arabic news sites loyal to Shiite-dominated Iran, the regional rival of Sunni Saudi Arabia.
Relations between the two countries have worsened this year.
“The newspaper online site was subject to hacking at 9:20 on Thursday morning (0620 GMT) by hostile groups from outside the kingdom,” the newspaper said in a statement obtained by AFP.
“They were able to control the site for a period of time and published false news” including a fake statement by Crown Prince Mohammed bin Nayef, it said.
The hacker intentionally “published lies”, claiming they were quotes from Prince Mohammed.
He was cited as saying the Saudi-led military coalition’s operation in Yemen had gone on longer than expected, comments which Al-Watan said were “not based on any reality.”
The coalition began air strikes in Yemen in March last year to support the government of President Abedrabbo Mansour Hadi after Huthi rebels backed by Iran seized much of the country.
A fragile truce has been in effect for almost two months while United Nations-brokered talks between the rebels and government take place in Kuwait.
Al-Watan is a privately-owned newspaper linked to a member of the royal family and based in the southwestern city of Abha.
It said technicians were able to recover the website after “this crime” of hacking.
Riyadh cut ties with Tehran in January after demonstrators torched its diplomatic missions there following the execution of a prominent Shiite cleric in Saudi Arabia.
In their latest dispute, the two countries have not been able to agree on arrangements for Iranian pilgrims to join the annual Muslim hajj in Saudi Arabia this year.
Four years ago, a damaging malware assault hit the state oil company Saudi Aramco. US intelligence officials believed it was linked to Iran.
Tehran last month denied supporting cyber attacks against the United States after a New York court indicted seven Iranians over hacking dozens of American banks and a major dam.