President-elect Donald J. Trump said Friday that his inauguration would be moved inside the Capitol Rotunda because of a frigid weather forecast, the first time in 40 years that a presidential swearing-in will be held indoors.

The change for Monday’s inauguration means that far fewer people will be able to watch in person as Mr. Trump officially becomes the 47th president. It also avoids the potential for smaller crowds because of the weather. Mr. Trump was furious about reports that he had smaller crowds in 2017 than President Obama had at his 2009 inauguration.

“The weather forecast for Washington, D.C., with the windchill factor, could take temperatures into severe record lows,” Mr. Trump wrote on his social media website, Truth Social.

“I don’t want to see people hurt, or injured, in any way,” he added. “It is dangerous conditions for the tens of thousands of Law Enforcement, First Responders, Police K9s and even horses, and hundreds of thousands of supporters that will be outside for many hours on the 20th (In any event, if you decide to come, dress warmly!).”

Trump officials had been discussing what to do about the weather well before Mr. Trump decided to have the inauguration moved indoors.

Temperatures in Washington on Monday are projected to drop to a low of 11 degrees, with a high of 23 degrees. The last time a swearing-in moved indoors was in 1985 for President Ronald Reagan’s second inauguration, similarly because of cold weather.

Mr. Trump said many of the people who have been streaming into Washington to watch the festivities can gather to watch inaugural events at the 20,000-seat Capital One Arena, which is several blocks from the National Mall, and that he would join them there afterward.

That is likely a bitter pill to swallow for some major donors, who paid top dollar to come to the swearing-in and witness it in person. Trump officials received calls from donors on Friday asking for help getting access. The Rotunda only seats about 600 people, according to a spokesperson for the Joint Congressional Committee on Inaugural Ceremonies.

The inaugural parade is also expected to be incorporated into the viewing party at the arena, according to Mr. Trump’s social media post. It is unclear whether additional ways to watch — such as Jumbotrons outside the arena — will be available.

While Mr. Trump’s inaugural events were set to be the highlight of the weekend, many donors and corporate executives have made plans to fly into the capital for the preceding days. None of the other events are likely to be affected.

Some major donors, who tend to be older, were not even planning to watch the ceremony outdoors before Mr. Trump’s Friday decision. One donor group, the Rockbridge Network, planned to host what was described as an indoor viewing party for the ceremony and parade at The Ned, a new members club in Washington.

If any donors are dissuaded from coming to Washington because of the new location, there are plenty of people willing to take their seats. Throughout January, some donors were so desperate that they made donations to the presidential inaugural committee without a guarantee that they would get tickets at all, and sometimes were placed on wait-lists.