Midfielder Iniesta, who had only recently shaken off a thigh problem, had to be substituted in the 77th minute after a heavy challenge while fullback Ramos fell awkwardly and hurt his ribs.
Coach Vicente del Bosque said Iniesta was fine and had only been in slight pain while tests on Ramos at the European champions' training base showed no bone damage, the Spanish football federation (RFEF) said on their website.
"The player (Ramos) had sore ribs after a bad fall in the Switzerland match," the federation said. "According to the medical examination conducted in Potchefstroom, (he) did not have any damage to the bone."
Spain had injury worries before the tournament, particularly striker Fernando Torres and midfielder Cesc Fabregas, but they are now fully fit, said the team's medical staff.
Del Bosque used Torres as a second-half substitute on Wednesday but left Fabregas on the bench and brought on wingers Pedro and Jesus Navas to join Torres and David Villa up front.
Fabregas told Marca radio on Thursday he was not getting the playing time for Spain he would like but that would not affect his commitment.
"For the previous coach I was the 12th man... but the current coach sometimes chooses other players," he said.
"I am not getting the minutes I would like but that does not affect my attitude. I am still competing (for a place) whether I play or not."
The 10 outfield players who started Wednesday's match mostly worked in the gym on a chilly Thursday evening in Potchefstroom, with the three goalkeepers and the remaining 10 squad members training outdoors in front of several hundred noisy locals.
Spain can get their World Cup campaign back on track when they play outsiders Honduras, who lost 1-0 to Chile, in their second Group H match on Monday in Johannesburg.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
