Mr Chauvin, a 19-year police veteran, did not enter a plea as he appeared via teleconference on Monday.
He did not speak during the 15-minute hearing, and was handcuffed and wearing an orange jumpsuit as he sat a small table.
Judge Jeannice M Reding set a bail of $1.25m with no preconditions, or $1m with conditions that include Mr Chauvin not contacting Mr Floyd's family, surrendering his firearms and not working in law enforcement or security as he awaits trial.
His lawyer did not object to the bail price.
Mr Chauvin, 44, is currently being held at the Minnesota state prison in Oak Park Heights, after being transferred several times.
His next court appearance is set for 29 June.
What are the accusations against Chauvin?
He faces three separate charges: unintentional second-degree murder, third-degree murder and second-degree manslaughter, for which the maximum penalties are prison terms of 40, 25 and 10 years respectively.
By bringing multiple charges, prosecutors give jurors a choice and increase the chances of a conviction.
Minneapolis city council has voted to ban chokeholds and neck restraints by police officers, and Democrats in Congress have unveiled sweeping legislation on police reform.
In France, which saw Black Lives Matter protests over the weekend, Interior Minister Christophe Castaner announced that police would no longer be allowed to use chokeholds to arrest people.
France's police watchdog has revealed that there were 1,500 complaints against officers last year, half of them for alleged assaults.
How are people in Houston mourning Floyd?
Masked and gloved mourners have been filing past Mr Floyd's coffin in line with coronavirus social distancing requirements, with only 15 guests allowed in the church at a time.
Anti-racism protests started by Mr Floyd's death are now entering their third week in the US. Huge rallies have been held in several cities, including Washington DC, New York, Chicago, Los Angeles and San Francisco.
With the rallying cries "Black Lives matter" and "No Justice, No Peace", the demonstrations are among the largest US protests against racism since the 1960s. Saturday's gatherings included a protest in the Texas town of Vidor, once infamous as a stronghold of the Ku Klux Klan white supremacist group.