Cuttitta had been admitted to hospital in Rome with Covid-19, and the Italian rugby federation confirmed his death on Sunday evening.
He passed away from complications of Covid, just two days after his mother had died from the virus.
Cuttitta played 70 times for Italy between 1990 and 2000 and captained the Azzurri on 22 occasions.
He spent time playing for Harlequins and served as Scotland’s scrum coach for six years from 2009. He left the Scotland set-up in 2015, and went on to work as a coaching consultant with Romania, Canada and Portugal.
Townsend, the Scotland head coach, said: “This is such sad news, and my thoughts go out to Massimo’s family at this tragic time for them.
“Mas was a lovely man who connected really well with players and fellow coaches, building lasting relationships with a huge number of people in Scottish rugby and throughout the world.
“His passion and expertise made a game-changing impact at improving the scrummaging of the national team and both of our pro teams. He developed a strong bond with his beloved front row forwards, who I’m sure will be immensely grateful for having met and worked with him. Rest in peace Massimo.”
Prior to his role with the Scotland team, Cuttitta had worked with Edinburgh Rugby as a consultant in 2005 and for the next few years his scrummaging expertise was utilised by both Scottish pro-clubs.
It was during Andy Robinson’s spell as Scotland head coach that the Italian was brought into the national set-up and he made a huge contribution, notably on the 2010 tour of Argentina when Scotland won both Test matches against hosts with a reputation as formidable scrummagers.
A statement from the SRU said: “Scottish Rugby is deeply saddened to hear the passing of our former Scotland scrum coach Massimo Cuttitta.
“Our thoughts are with his family and friends in rugby at this time.”
Edinburgh Rugby said: “Desperately sad news. Massimo played a vital role in developing a number of the club’s players over the years and was one of the nicest, most genuine people you’re likely to meet. Rest in peace, you’ll be missed.”