Loop-mediated isothermal amplification (LAMP) is a method of nucleic acid amplification that is more stable and resistant to DNA amplification inhibitors than conventional PCR. LAMP multiplexing with reverse transcription allows for the single-tube amplification of several RNA fragments, including an internal control sample, which provides the option of controlling all analytical steps. We developed a method of SARS-CoV-2 viral RNA detection based on multiplex reverse-transcription LAMP, with single-tube qualitative analysis of SARS-CoV-2 RNA and MS2 phage used as a control RNA. The multiplexing is based on the differences in characteristic melting peaks generated during the amplification process. The developed technique detects at least 20 copies of SARS-CoV-2 RNA per reaction on a background of 12,000 MS2 RNA copies. The total time of analysis does not exceed 40 min. The method validation, performed on 125 clinical samples of patients' nasal swabs, showed a 97.6% concordance rate with the results of real-time (RT)-PCR assays. The developed multiplexed LAMP can be employed as an alternative to PCR in diagnostic practice to save personnel and equipment time.