A statement said the hastily arranged game would be staged at the Offenbach Kickers Stadium in Frankfurt [1830 GMT] and comes as a welcome boost to a Bafana squad battling to find suitable opposition.
The side, which has been training in Germany since early April with home-based players, was due to face China Wednesday after a 0-0 draw against fellow FIFA World Cup qualifiers North Korea.
But the Chinese withdrew from the fixture last Friday, citing travel problems in the aftermath of the European airspace closure crisis after volcanic ash drifted south from Iceland.
It will be the second game between Bafana Bafana and the Reggae Boyz of Jamaica in five months following a goalless draw in Bloemfontein last November.
South Africa return to Johannesburg at the end of this week, resume camp on 5 May and play friendlies against Colombia and Denmark before facing Mexico in the 11 June opening match of the World Cup.