Mbappé, 27, left the pitch in the 81st minute at La Cartuja after requesting a substitution, heading straight down the tunnel without waiting for examination by medical staff.
Gonzalo García replaced him as Héctor Bellerín then equalised in stoppage time to deny Madrid all three points.
Arbeloa was brief in his assessment of the injury afterwards. "I don't know, no idea. He felt some discomfort. We'll see how he progresses in the coming days."
El Chiringuito journalist José Luis Sánchez subsequently reported that initial checks pointed to a strain of the left hamstring — the same leg that caused Mbappé problems earlier this season. France face Senegal in their World Cup opener on 16 June, 53 days away.
Beyond the injury, Spanish radio station COPE has reported that Mbappé's relationship with Arbeloa is significantly cooler than it was with his predecessor Xabi Alonso.
The two men are described as having a purely professional relationship with no personal warmth, and last week's social media incident — where Mbappé liked a post promoting José Mourinho as the next Real Madrid head coach — and Arbeloa's icy response in the subsequent press conference illustrate the dynamic.
"The fact that people like Mourinho or Julia Roberts doesn't bother me," Arbeloa said. "It's not important to me."
Madrid are now eight points behind leaders Barcelona with six games remaining, with the title beyond reach. The draw also came a day after the club confirmed that Arda Güler and Eder Militão would miss the rest of the season with hamstring problems, though both are expected to be fit for the World Cup.