No, the Impossible Burger does not contain tree nuts or peanuts. The Impossible Burger does contain refined coconut oil. The FDA classifies coconut as a tree nut for food labelling purposes, but refined coconut oil is not considered an allergen.
Please exercise the same level of caution you would with any food. If you have a known allergy, please check with the restaurant about their use of that ingredient and cross-contamination risks.
Full Ingredient List:
Water, Textured Wheat Protein, Coconut Oil, Potato Protein, Natural Flavors, 2% or less of: Leghemoglobin (soy), Yeast Extract, Salt, Soy Protein Isolate, Konjac Gum, Xanthan Gum, Vitamin C, Thiamin (Vitamin B1), Zinc, Niacin, Vitamin B6, Riboflavin (Vitamin B2), Vitamin B12.
Contains: Soy, Wheat