The comments by deputy crown prince Mohammed bin Salman are seen as a challenge to Iran.
It has vowed to increase oil production following lifting of Western sanctions.
In the Bloomberg interview, the prince also spoke about his plan for a giant public investment fund.
Worth more than $2 trillion, it would be designed to reduce Saudi Arabia’s reliance on income from oil.
Part of the plan would be a sale of shares in the state-owned oil firm Aramco, which could start as soon as next year, according to the interview.
Iran will not take part in a conference in Doha on 17 April, where the freezing of oil output is due to be discussed.
"If all countries agree to freeze production, we will be among them," the prince told Bloomberg.
When asked whether Iran needed to be among those countries he said "without doubt".
Oil prices, which had edged into positive territory, fell after the Prince’s comments.
Brent crude fell $1.63 cents, or 4%, to $38.70 a barrel. Prices rose 6% in the first three months of this year - the first quarterly increase since a 15% rally between April and June 2015.
PVM Oil Associates analyst Tamas Varga said there had been high hopes about the impact of a possible production freeze, but he added: "It is hard to see how sticking to the January output level would be supportive for oil prices. There will be no rebalancing this year."
Shailaja Nair, of energy information provider, said the market was still oversupplied with crude and there was no possibility of demand increasing in the short term.
"Considering the amount of crude already in the market, a freeze is not going to make much difference."
A monthly survey by Reuters this week showed that oil output from the 13 Opec members rose in March on higher production from Iran and near-record exports from southern Iraq.
Iraq reported Opec’s biggest growth last year, producing more than four million barrels per day - making the cartel’s second-largest producer after Saudi Arabia.
In February, Saudi Arabia and Russia said they would freeze oil output at January levels if other producers followed suit. Oil prices have plunged from their recent peak of $116 in June 2014 because of oversupply and sluggish demand. –BBC