Rotterdam Police spokeswoman Patricia Wessels said police were called to a home in the port city in the early hours of the morning and found the 24-year-old Dutch player bleeding from a stab wound.
The officers and ambulance paramedics were unable to resuscitate Halman.
Wessels said the officers arrested Halman's 22-year-old brother. She declined to give his name, in line with Dutch privacy rules.
"He is under arrest and right now he is being questioned," Wessels told The Associated Press in a telephone interview. "It will take some time to figure out what exactly happened."
No charges have been filed in the case.
Mike Nicotera, Halman's agent, said in a statement: "This hurts."
"The loss of a talented 24-year-old young man like Greg, amid such tragic circumstances, is painful for all of us throughout the game," MLB commissioner Bud Selig said in a statement. "On behalf of Major League Baseball, I send my deepest condolences to the entire Mariners organization and to all those whose lives were touched by Greg."
Mariners chairman Howard Lincoln, president Chuck Armstrong and general manager Jack Zduriencik paid tribute to Halman on behalf of the club.
"Greg was a part of our organization since he was 16 and we saw him grow into a passionate young man and talented baseball player," they said in a statement. "He had an infectious smile that would greet you in the clubhouse, and he was a tremendous teammate. Our thoughts and prayers go out to Greg's family."
Halman hit .230 in 35 games and made starts at all three outfield positions for the Mariners in 2011 before being optioned to Triple-A Tacoma.
Because he played professionally in the United States, Halman was not part of the Netherlands team that won the Baseball World Cup in Panama last month. The Dutch beat Cuba 2-1 in the final to become the first European team to win the title.
Born in the city of Haarlem, Halman played in the Dutch Pro League and was part of the gold medal winning Dutch squad at the 2007 European Championship.
MLB Players Association president Michael Weiner said in a statement that the union was "deeply saddened" to learn of Halman's death.
"Greg was passionate about the game of baseball and generously gave of himself to share his passion with others in an attempt to help grow the sport's popularity across Europe. He will be sorely missed. Having played for the Netherlands in the 2009 World Baseball Classic, and having participated in the recent 2011 European Big League Tour, Greg's lasting legacy is sure to be the trail he helped blaze for European youth to follow in his footsteps," Weiner said in the statement.
Former major leaguer Robert Eenhorn, the technical director of the Dutch baseball association, said he was devastated by the news.
"The only thing I can say right now is we are deeply shocked," Eenhorn, who played for the New York Yankees and Anaheim Angels in the 1990s, told the AP. "All our thoughts are with his family and how they are going to have to deal with this tremendous loss."
Halman was in Europe this month as part of the European Big League Tour, an initiative organized by Baltimore Orioles pitcher Rick VandenHurk in which major leaguers gave clinics to children. VandenHurk also is Dutch.
"It's really sad and it's really terrible the way it happened," International Baseball Federation president Riccardo Fraccari said. "We mourn for him and respect his family's sorrow."
Massimo Fochi, the vice president of the Italian baseball federation, said he met Halman less than two weeks ago at a European Big League Tour event in Parma.
"He was a great guy and the most appreciated by the kids," Fochi said. "His passing away is really painful."
Information from The Associated Press was used in this report.