Lieutenant Rasczak saved him, according to other Roughnecks.
From the film's script, right after Johnny Rico is released from the healing chamber and he and Ace and Dizzy join Roughnecks. Here's the script's scene:
Ace: So, I hear your lieutenant is a real nut-buster
Birdie belts him, and Ace goes down.
Birdie: No one talks about the Lieutenant that way. He saved my life!
Sugar: Mine, too.
Other Roughnecks: Same for me. Me, too.
Ace: Well, sounds like he is quite a guy.
Birdie (to Johnny): Who do you think saved your ass?
("Starship Troopers" screenplay by Edward Neumeier, Production Draft 4/17/1996)
The comic adaptation wasn't that specific, it simply said "someone found him and stitched him up" and omitted that "saved your ass" scene.
Totally ironically, this is one of the small, insignificant plot details that the film script actually gets somewhat correct from Heinlein's book (while getting everything meaningful wrong) - RAH heavily implies that Lieutenant saved likely Rico's life in the book, if not physically then metaphorically:
I'm glad I did it that way, because if I hadn't, I wouldn't have been along when the Lieutenant bought it . . . and that would have been just too much to be borne. It happened very fast and just before retrieval. A man in the third squad was wounded, not badly but he was down; the assistant section leader moved in to pick up — and bought a small piece of it himself. The Lieutenant, as usual, was watching everything at once — no doubt he had checked physicals on each of them by remote, but we'll never know. What he did was to make sure that the assistant section leader was still alive; then made pickup on both of them himself, one in each arm of his suit.
He threw them the last twenty feet and they were passed into the retrieval boat — and with everybody else in, the shield gone and no interdiction, was hit and died instantly.
I haven't mentioned the names of the private and of the assistant section leader on purpose. The Lieutenant was making pickup on all of us, with his last breath. Maybe I was the private. It doesn't matter who he was. What did matter was that our family had had its head chopped off. The head of the family from which we took our name, the father who made us what we were.
("Starship Troopers" by Robert Heinlein, Chapter 10)
However, the movie's "Lieutenant Rasczak" character was actually a rather poor amalgamation of three different book characters, Rico's MP teacher (Col DuBois), his first commander (Lieutenant Rasczak) and Sgt/Lt Jelal.