Strikes are planned for Thursday, Saturday and Sunday in an ongoing dispute between ScotRail and the RMT union over driver-only trains.
The train operator will provide extra services to Troon, South Ayrshire, throughout Thursday to Sunday for the thousands of spectators attending the championship.
Mr Yousaf said: “These rail strikes are continuing to inconvenience people right across the country.
“It’s particularly disappointing that they are falling on the week of the Open Championship, which is one of the highlights of Scotland’s sporting calendar.
“However, rail passengers should note that travel planning is well advanced with ScotRail offering an enhanced timetable above the regular provision.
“More services and carriages will run between Glasgow Central and Troon throughout Thursday to Sunday to allow the vast majority of people to travel to and from the venue with minimum disruption to travel plans.
“The National Traffic Control Centre is being staffed in order to monitor the travel situation during the week and over the weekend, and make sure that the tournament organisers, transport providers and the public are kept well informed throughout.
“I would recommend that people wishing to travel to Troon via train check the latest advice from ScotRail using the live journey planner on their website or their app and leave plenty of time for their journey.”
Several days of industrial action have already been held and the conciliation service Acas has been involved in trying to resolve the dispute, but it remains deadlocked.
The union said it is defending its policy of no extension of driver-only trains and for guards to be in control of operating doors.
ScotRail insists there will be no job losses or pay cuts with its proposed changes.
“These strikes are disrupting passengers and affecting the reputation of Scotland’s railways, and they should be suspended to allow talks to conclude and a way forward agreed,” Mr Yousaf added.