When The Grass Dancer came out, praise for Power's work was almost unanimously favorable. Power won the 1995 PEN/Hemingway Award for the best first fiction of that year, and received glowing reviews. All the reviewers were fascinated by the window into Sioux culture that the book provided, praising Power's depiction of her Native American heritage as much as they praised her vivid, mesmerizing prose style. In Publishers Weekly, a reviewer wrote, "a major talent debuts with this beguiling novel," and praised Power's use of historical events such as the Apollo moon landing and the great drought on the plains during the nineteenth century, along with supernatural and spiritual events, "reinforcing the seamless connection" between these two realms. Calling her "a consummate storyteller," the reviewer also praised her use of suspense, humor, irony, and drama, and wrote, "Seduced by her humane vision and its convincing depiction, one absorbs the traditions and lore of the Sioux community with a sense of wonder."

In the New York Times Book Review, Lawrence Thornton remarked that Power "writes with an inventiveness that sets her writing apart from much recent American fiction ... Written with grace and humility, The Grass Dancer offers a healing vision that goes to the core of our humanity." Stephen Henighan wrote in the Times Literary Supplement that "this scrupulously wrought novel, deftly fusing traditional story-telling with the forms of contemporary fiction, provides a sparkling demonstration of that [Sioux] culture's continued vitality."

Caroline Moseley wrote in the Princeton Weekly Bulletin that the novel was "a mesmerizing tale," and that "the numinous power of the spirit world illumines the novel; the narrative flows forward and backward in time, and dead forbears—such as the 19th-century lovers Ghost Horse and Red Dress—are vital presences in daily life."

Dani Shapiro in People Weekly praised Power's musical, magical prose style, and in The Bucknellian, Anne Putnam praised the insights embodied in Power's work, which add a deeper dimension to the novel than exists in most current work.

Robert Allen Warrior, an Osage writer, was one of the few critics whose assessment of the book was not unequivocally favorable. He praised the author's "strong debut," but tempered this by remarking, "The novel exudes youthfulness, both in terms of tremendous energy and some telling unevenness, but this is a writer to watch for in the future." Warrior did not specify the nature of the "unevenness," but summed up by writing that "The Grass Dancer is a sometimes brilliantly told story that is well worth reading." He also drew hope from the fact that Power is clearly influenced by the excellent Native American writers who have preceded her, most notably Louise Erdrich Leslie Marmon Silko and Joy Harjo, and wrote that, clearly, "new writers are learning from those who have already trod the difficult path of realizing artistic vision and are ... honoring that earlier work."