The 23-year-old academy graduate only made a total of 18 first-team appearances for the county following his debut in 2011, and did not play a first-class game in 2015.
"Saying goodbye to a man who has come through the club's youth structure is not something we enjoy doing," managing director of cricket Angus Fraser said.
"The lack of first-team opportunities has frustrated him."
Sandhu featured five times for Middlesex this year, with all of his appearances coming in one-day competitions.
"Gurjit is fit, strong and capable," added Fraser.
"I believe he has the potential to play far more first-team cricket at another club than he has for us and hopefully he will get those opportunities elsewhere."

Cheap Trick, and Steve Miller also made the 2016 list, but Chic - nominated for a record tenth time - missed out on the honour.
The five acts were chosen by fans and more than 800 voters of the Rock and Roll Hall of Fame Foundation.
They will be inducted into the Hall of Fame in a ceremony in April.
To be eligible, artists or bands need to have released their first single or album 25 years ago.
Others who were nominated this year but didn't make the cut include Janet Jackson, Nine Inch Nails and The Smiths.
It was the fourth time rap stars NWA - the subject of this year's hit biopic Straight Outta Compton - had been nominated.
Led by Dr Dre and Ice Cube, NWA are described as "unexpected, shocking, flawed, revolutionary and worthy," by the Rock and Roll Hall of Fame.
"NWA's improbable rise from marginalized outsiders to the most controversial and complicated voices of their generation remains one of rock's most explosive, relevant and challenging tales", it said.
It was the third nomination for British metal band Deep Purple.
A statement from the organisers said: "Deep Purple's non-inclusion in the Hall is a gaping hole which must now be filled," calling them "the Holy Trinity of hard rock and metal bands" along with Led Zeppelin and Black Sabbath who are already inductees.
Seventies rock band Chicago, led by Peter Cetera is also an omission according to organisers.
"Chicago's early line-up created such an unmistakable sound and their inclusion into the Rock and Roll Hall of Fame is not only well-deserved, but an honour that has been overlooked.
"With over 21 top 10 singles, five consecutive number one albums, 11 number one singles - fans that stretch across the globe and countless bands that have followed in their wake, Chicago's legacy is unquestionable."
Steve Miller and Cheap Trick are first time nominees.
Earlier this year, Green Day, Lou Reed, Joan Jett & The Blackhearts and Ringo Starr were among those inducted into the Hall of Fame as the class of 2015.
Middlesex have released left-arm seamer Gurjit Sandhu.
[NEXT_CONCEPT]
Ground-breaking rap act NWA, Deep Purple and Chicago have been announced as inductees of the Rock and Roll Hall of Fame.