Vice President Joe Biden was originally set to have led a delegation to Saudi Arabia on Obama's behalf.
However, the schedule for the President's departure from India has been adjusted to allow Obama to stop in Riyadh himself on his way home, White House press secretary Josh Earnest said.
Funeral services were held Friday
for King Abdullah bin Abdulaziz al Saud, who died earlier that day. He was 90.
World leaders are now traveling to the Saudi capital, Riyadh, to offer condolences for Abdullah's death and pay their respects to the new ruler.
Abdullah was seen by many as a cautious reformer who succeeded in securing broader freedoms in the conservative kingdom, but fell short in gaining greater independence for women.
His successor, who is 79, faces a number of challenges as he takes up the reins, including Iran, the rise of ISIS, the crisis in neighboring Yemen
and the drop in oil prices.
But Salman has plenty of experience to draw on, having served as defense minister and deputy prime minister of Saudi Arabia, a vital U.S. ally in the Middle East. Like Abdullah, he is one of the dozens of sons of Saudi Arabia's founder, King Abdulaziz.
No Taj Mahal visit
On Monday, he will become the first American president to headline India's Republic Day parade, standing beside Indian Prime Minister Narendra Modi.
Earnest said Obama's schedule had been changed in coordination with the Indian government and that he would now be leaving India after giving a speech on Tuesday.
"The President regrets that he will be unable to visit Agra during this trip," Earnest said. Agra is where the spectacular Taj Mahal mausoleum is located.
Biden will now remain in Washington rather than go to Saudi Arabia.
Although no reason for the change of plan was given, it follows criticism this month of the Obama administration for its failure to send a senior representative to France for a huge unity march held in the wake of the Paris terror attacks.
The administration admitted it erred
and dispatched U.S. Secretary of State John Kerry to Paris the following week to offer the United States' support and condolences.
Speaking to CNN's Richard Quest in Davos, Switzerland, on Friday, Kerry said he expects no changes in his government's relations with Saudi Arabia with the change of kings.
"I don't anticipate anything based on the conversation we have had, no," he said.
Jordan's King Abdullah and Egypt's President Abdel Fattah al-Sisi both left Davos early to attend the funeral on Friday.
In line with custom, Abdullah was laid to rest in an unmarked grave in a brief and simple ceremony after funeral prayers in Riyadh's Imam Turki Bin Abdullah Grand Mosque.