The state's 14 delegates will be awarded proportionally. Mr Sanders has won seven of the latest eight states.
However rival Hillary Clinton maintains a clear lead in the overall race. Both are concentrating their efforts on the key New York primary later this month.
In the Republican race, Ted Cruz hopes to pick up more delegates in Colorado.
In state assemblies which culminated on Friday, Mr Cruz won 21 delegates to just two for Donald Trump, who still has a comfortable lead in the overall nomination race for the Republicans.
On Saturday, a further 13 delegates are at stake at the Colorado Republican Convention.
Mr Cruz has 520 Republican delegates to 743 for Mr Trump. Mr Cruz is hoping to win at least enough votes to block an outright win for Mr Trump and force a decision at the party's convention in July.
The next big prize for both parties is the New York primaries on 19 April: 291 delegates are at stake for the Democrats and 95 for Republicans.
Despite Saturday's win in the Wyoming caucuses, Mr Sanders still has only 1,061 delegates to 1,749 for Mrs Clinton, when the latter's 469 superdelegates are added to the tally. To win, a candidate needs 2,383.
The presidential election itself, on 8 November, will see America vote for a successor to Barack Obama, a Democratic president standing down after two terms in office which have seen the Republicans take control of both houses of Congress.
19 April: New York primary
26 April: Primaries in Pennsylvania, Connecticut, Delaware, Maryland and Rhode Island
Bernie Sanders has won the latest stage in the battle for the Democratic nomination in the US presidential poll by securing victory in Wyoming.