The Cherries have appointed Jonathan Woodgate as their manager until the end of the season.
Henry will now be available after returning to London for personal reasons.
Henry said in a statement: "It is with a heavy heart that I've decided to take this decision. The last year has been an extremely difficult one for me personally.
"Due to the worldwide pandemic, I was unable to see my children. Unfortunately due to the ongoing restrictions and the fact that we will have to relocate to the US again for several months will be no different. The separation is too much of a strain for me and my kids.
"Therefore, it is with much sadness that I must take the decision to return to London and leave CF Montreal. I would like to thank the fans, players and all the staff of this club that have made me feel so welcome."