The midfielder was arrested after a Range Rover crashed in Mere, Cheshire, in the early hours of Monday.
Two women and a man were treated at the scene for minor injuries, Cheshire Police said.
Mr Drinkwater, 29, of Nether Alderley in Cheshire, was released on unconditional bail to appear at Stockport Magistrates’ Court on 13 May.
Police were called to reports of a one-vehicle crash on Ashley Road in Mere at 00:30 BST and arrested the footballer.
The former Manchester United trainee won the last of his three England caps in 2016.
Danny Drinkwater profile
Danny Drinkwater was a product of the Manchester United youth academy but did not make a senior appearance for the club, spending loan spells at Huddersfield, Cardiff, Watford and Barnsley before joining Leicester in 2012.
The midfielder was named in the Championship Team of the Year as the Foxes won promotion to the Premier League in the 2013-14 season.
He remained a key part of the Leicester side as they overcame odds of 5,000-1 to win the Premier League under Claudio Ranieri in 2015-16.
His performances during the Foxes’ remarkable title-winning campaign earned him a first England call-up, making his debut against the Netherlands at Wembley in March 2016 and going on to win three caps to date.
However, having asked to leave the club, he joined Chelsea in a £35m deal in September 2017, following former team-mate N’Golo Kante to Stamford Bridge after the midfielder’s move the previous summer.
The 29-year-old played 22 times in all competitions as injury disrupted his first season with the Blues and he has found himself frozen out under new boss Maurizio Sarri this term, with his only appearance coming in the Community Shield.