Which is the correct sentence?

sure...

Thanks.

Yes, both are fine, but it's better style to say "He gave Ali an injection" in this case.

To make a slightly finer point, if you give something "to" someone, then you are probably handing something over

e.g. Molly gave her coat to Tom. (that is, to him and nobody else)

and

Molly gave Tom her coat. (the emphasis here is on the coat)

Re: Which is the correct sentence?
Depends what Ali thought about being injected

come to think of it, "the injection" sounds better than "an injection"...