Burns, 22, entered Thursday's game against the Edmonton Oilers with three goals - tops in the team among blue-liners - and one assist in nine games. Burns, who will make US$875,000 this season, was set to become a restricted free agent next summer.
Terms of his new contract were not released.
"The effort Brent has given to improving himself as a player is evident to the point that he is becoming an impact player in our lineup," Wild general manager Doug Risebrough said in a statement. "This is recognition of that effort and of his potential."
Burns has 15 goals and 36 assists in 194 career games with the Wild, who selected him in the first round (20th overall) of the 2003 draft.