To ensure confidentiality, medical information is usually encrypted before it is sent to a third party for processing. Encryption technology can protect the privacy of data, but it limits the ability to search for data. The problem is usually solved by using public key encryption with keyword search (PEKS). Recently, some certificateless PEKS (CPEKS) schemes have been proposed. Not only do they allow users to search encrypted data, but they do not have the problems of certificate management and key escrow. However, they rely on the high-consumption bilinear pairing, and some of them are vulnerable to Inside Keyword Guessing Attacks (IKGA). To address these issues, we design a lightweight CPEKS scheme for the Medical Internet of Things (IoMT) that does not include bilinear pairing. In the random oracle model, our scheme is proved to be secure. The analysis results show that the proposed scheme has better overall performance than the existing schemes according to the security property, computation cost, and communication cost. Finally, an IoMT application scenario of our scheme is given.