The 77-year-old singer and musician, who co-founded the Beach Boys, gave an at-home performance of the 1988 song Thursday.
"I just want you to know that we're all in this together," Wilson said before starting the song.
"Love and Mercy" appears on Wilson's debut, self-titled solo album and his followup, I Just Wasn't Made for These Times.
Wilson also performed the Beach Boys song "God Only Knows," which appears on the band's 1966 album, Pet Sounds.
In April, Wilson rescheduled his European tour to 2021 due to the coronavirus (COVID-19) pandemic.
Wilson has struggled with physical and mental health issues for years. He resumed touring in fall 2019 after postponing his summer tour due to feeling "mentally insecure."
"It is no secret that I have been living with mental illness for many decades," the singer said in June 2019. "There were times when it was unbearable but with doctors and medications I have been able to live a wonderful, healthy and productive life with support from my family, friends and fans who have helped me through this journey."