No, Muslims do not believe in reincarnation. Reincarnation is the belief that a soul is reborn into a new body after death, and this concept is not a part of Islamic theology. In Islam, the belief in the afterlife is centered around the idea of resurrection and judgment.
Muslims believe in the Day of Judgment when all individuals will be resurrected, and their deeds will be judged by Allah (God). Depending on their faith and deeds, individuals will be either rewarded with entry into Paradise or punished in Hell. This belief is in accordance with the teachings of the Quran and the sayings of the Prophet Muhammad (peace be upon him).
The concept of reincarnation contradicts the Islamic understanding of the soul's journey after death and the finality of human existence. In Islam, each person has one life on Earth, and the afterlife is determined by their actions in this singular life.