A statement from selection convenor Haroon Lorgat on Tuesday said Tests on the left-arm spinner had "provided no clarity on his condition.
"Nicky has been released to go home to undergo further medical checks under the care of his own doctors."
Boje did not take the field after tea on Monday after the breathing problems he developed on the first day of the Test recurred.
"I wanted to be part of a winning team, but health problems have to be sorted out," Boje said.
Lorgat said Boje would not be replaced in the South African squad for the five-match one-day series which starts in Kingston, Jamaica, on Saturday.
"The squad has sufficient depth from which we can draw on," he said.
"This represents a good opportunity for fringe players to take advantage."
One of those players could be all rounder Justin Ontong, who arrived in St John's with Justin Kemp on Tuesday for the one-dayers.
Ontong and Kemp will join the squad in place of batsman Jacques Rudolph and fast bowler Monde Zondeki.
