The outcome means Obama will win most of the 12 delegates at stake, a tiny number compared to the 2,025 needed to secure the Democratic Party's presidential nomination at its August convention.
In 23 caucuses around Wyoming, Democrats, who make up about 25 per cent of the staunchly Republican state's electorate, chose between Clinton or Obama.
Officials reported large turnout in a state known for its Republican sympathies.
"I didn't know there was this many Democrats in the whole state," said Dick Sadler, a party official.
After Wyoming, Obama and Clinton will face voters in the southern state of Mississippi, where 33 delegates are at stake.
The campaign will then move to Pennsylvania on April 22.
Obama is favoured to win Mississippi.
His current delegate count stands at 1,581 to Clinton's 1,460.