The three-times Major winner said he was unaware the deer-antler spray, which he has been using for a couple of months, contained an insulin-like growth factor that is banned by the US circuit.
O'Meara, competing at the Dubai Desert Classic where the 56-year-old opened with a five-under-par 67 on Thursday, said he had a lot of respect for his friend Singh but that his situation should be no different to those who have been banned before.
"Probably he should be suspended for a couple of months, and I don't know what the US Tour Commissioner is thinking, but people have had to pay the price before and he should be no different," O'Meara said.
"I was a bit surprised to hear what Vijay said. I don't think he's a guy that would take advantage of anything, and besides I like Vijay. I wish the best for him and his family and I wish the best for him."
Singh, 49, allegedly paid one of the owners of Sports with Alternatives to Steroids (SWATS) $9,000 in November for the spray and other products, Sports Illustrated said this week.
Singh released a statement on Wednesday at the Phoenix Open confirming he had taken it, that he was "shocked" and "angry" at himself and that he was in cooperation with the tour over the issue.
Since the US Tour's anti-doping programme was launched in 2008, American journeyman Doug Barron is the only player who has been suspended for a violation, in November 2009.
Barron, then 40, was banned for a year for taking a performance-enhancing drug.
In keeping with honesty in golf, O'Meara said he had no doubts over Singh, who is known for his workaholic approach to the game.
"Has Vijay tried to bend the rules? No I don't think that."