The midfielder received threatening tweets after a 4-3 loss at home last week to the Colorado Rapids. A late turnover by Arnaud set up Colorado's winning goal in stoppage time.
Arnaud retweeted one message from SBarbosa17 that said: "I hope your family dies in a fire." The author of the message appears to be a local soccer fan.
Arnaud answered: "Wow. I know we lost and I made a mistake but I deserve this? I forgive you."
Other tweets that the team said he received from the same person appear to have been deleted.
The Impact and MLS filed a complaint with police, who have opened an investigation and will interview the individual.
"The Impact is taking this incident very seriously and will not accept threats of any kind made by individuals in regards to its players coaches or administrative staff in order to ensure their safety," the team said in a statement.
Arnaud, who is married and has a young daughter, did not comment.
His teammate Patrice Bernier called the threats unacceptable.
"You can have your opinion on a performance, good or bad," said Bernier. "But when it passes the line and there are threats against your family, even though people may say they're joking around, I don't think it's something that you can joke around with.
"You never know what could happen. People have to have (responsibility) for their words, what they say or what they put out on Twitter or social media. It's important that they realize that you can't just go out and make blatant attacks on a person or his family or anybody else."
Bernier said he, Arnaud and other Impact players got messages from fans deploring the death threats.
"At least they showed pride and they know this has a negative impact on the image of Montreal fans and the Montreal Impact," he said.
Threatening behaviour from fans could deter good players from signing with the Impact because "even if it's just words, you never know," he added.
Coach Marco Schallibaum supported the team's decision to go to the police.
"You can't accept a person who gives difficulties to a family," the Swiss coach said. "He makes a mistake maybe on the field, but you can't make this against him."
The Impact (9-4-4) are in first place in the Eastern Conference midway through the regular season.
The 33-year-old Arnaud was acquired in a trade with Kansas City ahead of the Impact's expansion season in 2012 and became the club's first captain in MLS.