Jesus, 19, was replaced by Sergio Aguero after 14 minutes at the Vitality Stadium after appearing to twist his right ankle while making a run towards goal.
Speaking after the match, Guardiola confirmed that the Brazilian striker will undergo tests to assess the extent of the injury on 14 February and said that he hoped it was not too serious.
"Tomorrow morning we will know exactly," Guardiola told City's official website. "Hopefully – I will pray tonight – it will not be a big issue."
Jesus joined City from Palmeiras for £27m ($34m) plus add-ons in August but stayed with the Brazilian club until the end of the domestic season in December.
He scored in his first two starts for City – against West Ham and Swansea City, respectively – and spearheaded the visitors' attack against Bournemouth, with Aguero forced to settle for a place on the bench.
Raheem Sterling opened the scoring at the Vitality Stadium before Tyrone Mings deflected substitute Aguero's effort into his own net to bring City within eight points of league leaders Chelsea.
Guardiola said he was pleased with his team's performance but insisted that the gap with Chelsea was too big to close with just 13 games left to play. Chelsea are now eight points clear of City.
"I was especially pleased with the performance, that's why we got the result. We could have scored more goals so we played a good game in one of the toughest games away," the Spaniard said.
"We know how the gap between all the teams is so close, between second and sixth. Today we started the game in fifth position in the Premier League and now we are second so it means everybody is there.
"It's so up and down and you know if lose you a game you are going to be down so it will be a good battle to qualify for the Champions League next season."