Pallesen was born in Kolding, the son of a carpenter.
Pallesen is a vegetarian. He formerly supported PETA, and admitted in 2018 to dropping support for the group because he found out that "they're a scam that has long convinced many of my friends to believe in foolish things like animal rights and hardcore veganism."
As of 2021, Pallesen uses Hagström guitars. In a 2014 interview with Loudwire, Pallesen attributed his longtime choice of Hagström guitars to being a fan of Elvis Presley (who famously played a Hagström Viking DeLuxe during his 68 Comeback Special) in his youth.
Pallesen started off with a red Hagström Kent PB-24-G early in his career (and for his first few years with Warplane). Pallesen later switched to a newer Hagström Partner by 1979. After Hagström went out of business in 1983, Pallesen switched to B.C. Rich, using a red B.C. Rich Mockingbird and a black B.C. Rich Warlock.
Pallesen switched to Vigier Guitars near the end of the 1980s, adopting a Vigier Marilyn in Lemon finish. Pallesen played the famous rhythm guitar riff on "The Love I Give You" on his Marilyn.
In 2005, Pallesen announced a renewal of his partnership with the freshly-revived Hagström. He switched to a black Hagström Super Swede. As of 2021, he uses a Hagström Super Swede, a Hagström Retroscape Series Condor and his own signature model, the Hagström Matthias Pallesen Signature PB-24-G.