The bearded Sikh was called a "stupid Indian" during a tour match against New South Wales at the Sydney Cricket Ground on Sunday, the Daily Telegraph said on Tuesday.
The incident comes after Australian cricket authorities warned fans that "idiots" would not be tolerated at the grounds in the wake of racial abuse hurled at South African players during a tour earlier this year.
The Daily Telegraph reporter said he witnessed a fan yelling at Panesar as he fielded near the boundary fence.
"Give us a wave Monty," the spectator shouted. "You can't speak English you stupid Indian, I'll have to say it in Indian.
"What are you doing playing in the English side, you're not English."
The paper said Panesar and South African-born Kevin Pietersen were also reportedly abused while playing against the Prime Minister's XI in Canberra last week.
England recognised that the first Sikh to play Test cricket for the country could be singled out for abuse in Australia, and Panesar underwent counselling from team psychologist Steve Bull before the tour began.
The rivalry between both sets of fans is expected to be intense during the sell-out series, with the tourists receiving vocal backing from the "Barmy Army" and the home fans itching to revenge last year's defeat in England.
But Cricket Australia has warned that action would be taken against anyone who misbehaved at the matches.
"No doubt there will be some idiots over the summer who do the wrong thing but we can assure fans that we will do all we can this season and in subsequent seasons to make their day the best it can be," said chief executive James Sutherland.