Jones said "the terrorist has got another wicket" when the bearded Hashim Amla took a catch to dismiss Sri Lankan batsman Kumar Sangakkara during the fourth day's play of the second Test in Colombo Monday.
Broadcaster Ten Sports, the Dubai-based TV company covering the series, sent the former Australian batsman home after a complaint from Cricket South Africa (CSA) chief executive Gerald Majola.
A contrite Jones, who will reportedly keep his commentary position on Australian radio, described his moment of madness to reporters after landing in his hometown of Melbourne.
"I waited four or five seconds and I just turned around and made a stupid, ridiculous off-the-wall comment that unfortunately was picked up in the background and, as television people always know, the microphone is always live," Jones said.
However, he also appeared to suggest there was an element of bad luck to the affair, adding: "There was only one country in the world that didn't take the ad break live and that was South Africa. It was picked up by a few viewers."
Jones, 45, said he had written a full-page apology to Amla and the South African team, as well as saying sorry to the bowler directly.
"I got hold of Hashim Amla and I spoke to him for a certain amount of time," he said. "I gave him my sincerest apologies and he was gracious enough to accept it.
"He said 'I hope you get through this ugly situation that you are going through'."
Earlier, Jones told reporters in Colombo that he respected the Muslim faith and said: "The irony is that I am great friends with most of the Pakistan team and they are all Muslims."
Ten Sports said it had terminated Jones' contract as a freelance commentator -- believed to be worth 400-1,000 dollars per match day -- and had apologised to both the cricket community and its million of viewers over the outburst.
"We regard sport as a tool for spreading harmony and believe sport has no room for such an act." Ten Sports official Jude de Valliere told AFP.
However, Melbourne commercial radio station 3AW reportedly had no such qualms, saying the controversy would not affect plans to use Jones as a commentator for upcoming internationals Down Under, which include The Ashes against England.
"What happened in Sri Lanka would not have any bearing on what he'll be doing with us," 3AW program director Clark Forbes told smh.com.au.
The CSA's Majola had demanded Jones's suspension and apology in a statement issued in Johannesburg on Monday night.
"We take the strongest exception to this comment and will lodge an official complaint with the host broadcaster, Ten Sports, that employs him," Majola said in the statement.
"We will be asking for his immediate suspension and a full apology.
"The switchboards of both Cricket SA and SuperSport, that takes a feed of the broadcast to South African audiences, have been jammed with calls from some very angry people.
"This kind of racial stereotyping has no place in cricket and must be stamped on swiftly," Majola said, adding he will also report the matter to the International Cricket Council.
Jones played 52 Tests and 164 one-day internationals for Australia between 1984 and 1994 and was named the Wisden cricketer of the year in 1990.
The Ten Sports feed on the series was going out across Asia, Middle East, Africa, Europe, the Caribbean and North America, de Valliere said.
The same production company will also broadcast the limited-overs tri-series between Sri Lanka, India and South Africa in Colombo from August 14-29.