The BBC reports the singer died in Madrid surrounded by her family on Saturday morning.
Her bandmate Cristina Sevilla wrote on Instagram: "My dear Maria, a wonderful artist but above all my friend left us today.
"I can only thank so much love for how I have received from you."
Baccara experienced an unprecedented level of success with Yes Sir, I Can Boogie.
The song reached number one in the UK and across much of Europe and eventually went on to sell a whopping 18 million copies – making it the biggest selling single by a female duo of all time.
A clip of Scotland players singing the 1977 disco classic together went viral in the aftermath of the men’s team qualifying for their first major tournament in 22 years.
Mendiola told the Scotsman at the time she couldn’t quite believe it had risen to prominence again.
“I’m so happy. It was very unexpected. Everybody started to call: journalists, friends, fans, family. Oh my god.
"The phone has been non-stop, but I am delighted, it was such fantastic news."
Baccara broke sales records following the release of Yes Sir, I Can Boogie in the 1970s.
She said: “If I was waking up in the morning and somebody told me this had happened, I wouldn’t have said this is impossible.
"But these guys, the Scottish team they made it a reality. After 43 years, to get to number three is like a dream come true.
“I found Andy Considine’s video very funny. They are young guys, nice looking guys, and they done a great job.
"One of the first things I did was send a thank you on Instagram to Andy. I had to do it.”