Yes, Christmas can be celebrated on Sabbath. Christmas is an annual celebration of the birth of Jesus Christ. It is celebrated on the 25th of December every year. This date can fall on any day of the week. If it happens that 25th December falls on Sabbath, Christmas will be celebrated on Sabbath.
It is also good to know that the Seventh day Adventist church celebrate Christmas on Sabbath. So if Christmas (25th December) falls on Sabbath, the Seventh day Adventist Church will celebrate Christmas on the same day as they normally do.