No. In MLA style, when you are quoting a work, you should maintain the integrity of the original text whenever possible. If the pronoun in a passage you are quoting does not jar with the surrounding prose or confuse the reader, you can leave it as is. For example, even though the following sentence starts in the third person and switches to the first person in the quotation, the “I” in the quoted phrase is far enough from “Laurence” that it does not create an unpleasant jolt:

Laurence is boastful, repeating to his brother that the picture is “the best thing I’ve done yet” (Munro).

Work Cited

Munro, H. H. “The Bull.” The Literature Network, Jalic, 2000-19, www.online-literature.com/hh-munro/1797/.

If, however, the pronoun is unclear, you can replace it with one in square brackets that works better with the surrounding text, or—since brackets can be distracting—you can revise the sentence instead.