The U.S. Constitution says that the president shall from time to time report to Congress on the State of the Union. It doesn’t say that the president has to give a speech. It doesn’t say a State of the Union speech has to be in the House of Representatives.
The modern ritual of an annual State of the Union address in the well of the House of Representatives dates back only to Woodrow Wilson.
For this to happen, the House has to invite the president to come and speak. Without such an invitation, the president may not set foot in the House. Usually this invitation happens a few days before the scheduled address.
Nancy Pelosi just sent a letter to Trump saying they need to talk about rescheduling this event while the government is shut down. Or maybe, he can just submit a report in writing (which Thomas Jefferson and many other pre-20th century presidents did).