Portuguese international Dias, 24, was influential in central defence as City won a third title in four years.
He was named men’s footballer of the year by the Football Writers’ Association in May.
City boss Guardiola was named Premier League manager of the season for the third time in four years.
Dias, signed from Benfica for about £65m last September, made 32 league appearances for City over the season, playing a part in 15 clean sheets.
City won 23 of the league matches Dias played, as they also won the Carabao Cup and finished as runners-up in the Champions League.
The winner was decided by votes from the public on the EA Sports website, combined with those of the 20 Premier League club captains and a panel of football experts.
The other nominees were Manchester City’s Kevin de Bruyne, Tottenham’s Golden Boot winner Harry Kane, Manchester United’s Bruno Fernandes, Liverpool’s Mohamed Salah, Chelsea’s Mason Mount, West Ham’s Tomas Soucek and Aston Villa captain Jack Grealish.
Dias was also named in the Professional Footballers Association’s (PFA) Premier League Team of the Year, and is in contention to win the PFA Player of the Year award, which is announced on Sunday.
Guardiola beat fellow nominees Marcelo Bielsa, David Moyes, Brendan Rodgers and Ole Gunnar Solskjaer to the manager award, with public votes combined with those of a panel of football experts.
Having received the award in his two previous title-winning campaigns, 2017-18 and 2018-19, the City manager’s third win moves him level with Arsene Wenger and Jose Mourinho. Only Sir Alex Ferguson has won it on more occasions – 11 in total.