Ordinarily, the prime minister would not receive a foreign dignitary at the airport, but instead send an official or a junior government minister.
"A new chapter in bilateral relations," Raveesh Kumar, spokesman for the Foreign Ministry, posted on Twitter, hailing Modi "breaking protocol" with a photograph of the pair warmly clasping hands by the steps of the prince's plane.
Modi is due to hold talks on Wednesday with the crown prince, who has already visited Pakistan, where he also received a lavish reception.
Saudi Arabia is India's top supplier of crude oil but the two countries have expanded ties beyond energy, and their governments have agreed to build a strategic partnership, India's Foreign Ministry said last week.
During the trip, India is expecting the crown prince to announce an initial investment in its National Investment and Infrastructure Fund, a quasi-sovereign wealth fund, to help accelerate the building of ports and highways, an Indian official and Saudi state media has said.
The crown prince's trip began days after a suicide bomber killed 40 Indian paramilitary police in Kashmir in the attack claimed by the Pakistan-based Jaish-e-Mohammad (JeM) militant group.
New Delhi has accused Pakistan of having a hand in the bombing and vowed to punish Islamabad, which denies involvement.
During his visit to Pakistan, the crown prince said Saudi Arabia had signed investment agreements worth $20 billion.
He is scheduled to leave New Delhi on Wednesday night, India's Foreign Ministry said.