The decision includes Glasgow Warriors’ pre-season friendly against Ulster which was due to take place at Scotstoun on Friday evening and the summer Test between Scotland Women and Spain which was scheduled for the DAM Health Stadium on Sunday.
No decision has been made yet on Edinburgh Rugby’s game in Italy against Benetton, also due to be played on Friday evening. Scottish Rugby said it was awaiting “government guidance”.
All domestic league rugby has been suspended.
A statement issued by the SRU said: “As a mark of respect, and to acknowledge the sad passing of Her Majesty The Queen, Scottish Rugby has decided to suspend all domestic competitive matches this weekend.
“This decision also includes Scotland’s Summer Test v Wales on Sunday and the Famous Grouse Summer Pre-Season Challenge between Glasgow Warriors and Ulster on Friday evening.
“A decision on Edinburgh Rugby’s game in Italy against Treviso, also on Friday evening, will be made once further Government guidance is known.”
The Scottish Rugby Union has close links to the royal family through the Queen’s daughter, the Princess Royal, who has been the SRU’s patron for over 35 years and is a regular attendee at Scotland matches at Murrayfield.
Glasgow Warriors confirmed that their match with Ulster would not be rescheduled and that ticket holders would be refunded.
"As a mark of respect, and to acknowledge the sad passing of Her Majesty The Queen, The Famous Grouse Pre-Season Challenge between Glasgow Warriors and Ulster has been cancelled,” the club said in a statement.
“The match which was due to kick-off at 7.30pm on Friday (9 September) will no longer take place at Scotstoun Stadium.
“All match tickets will be refunded and Season Ticket holders in the North and Main Stands will receive more information in due course.
“At this time, the club gives its heartfelt condolences to the Royal Family.”
Speaking earlier on Thursday, Franco Smith, the Warriors’ new coach, had acknowledged that he might have to use some of the club’s early league games to fine-tune his preparations for the campaign as he staggers the reintroduction of his Scotland players following their involvement in the summer tour of Argentina.
Smith stressed it is important to look at the bigger picture, both in terms of the long season ahead and the welfare of his international players.
Glasgow had a large contingent involved in Scotland’s tour, including Ali Price, George Turner, Zander Fagerson, Matt Fagerson, Rory Darge, Scott Cummings, Rufus McLean, Ross Thompson, Sam Johnson and Jamie Bhatti .
They returned later to pre-season than their club-mates.
“We have a specific plan for the guys who came back late,” said Smith. “It’s not just for Glasgow’s benefit, it’s for Scotland’s benefit, and obviously for the players. We are sticking with the plan to prepare them physically for what’s ahead.”
Glasgow’s opening URC game is due to take place next Friday in Italy against Smith’s former club Benetton.
“We don’t want to be only at our best for the first game,” he said. “There is a long season ahead and I think the next seven weeks will need to be well managed. Players will have to come in. It’s about how we physically prepare that’s important. Obviously it’s a challenge but we always knew it was going to be like that.”