Alonso and Alpine condemn abuse of F1 steward
Bellot, also Spanish and the only female steward at the race in Austin, is carrying out the role again in Mexico City this weekend.
Renault-owned Alpine said on Twitter they were "disappointed to learn of the unacceptable harassment".
Alonso, who finished seventh in Austin last Sunday but was demoted to 15th after a Haas protest and then restored to the position after a further review in Mexico on Thursday, posted on Instagram.
"I strongly condemn the recent online abuse which has been directed at FIA race steward Silvia Bellot," he wrote.
"This type of hateful behaviour is unacceptable in sport and society. It is particularly deplorable that these comments are aimed at one of our sport's volunteers and officials."
Alonso had his U.S. Grand Prix points reinstated after stewards found race control gave rivals Haas the wrong advice about a deadline for making a protest.