Former presidents from both parties typically attend inaugurations (George W. Bush and Laura Bush will be there, as will Jimmy and Rosalynn Carter), but the presence of Hillary Clinton takes on added meaning, given that she was Trump's main opponent in the 2016 race.
She won the popular vote by more than 2.9 million votes, but Trump won the Electoral College, securing him the presidency.
The last time she and Trump were in the same room together was at the Al Smith Dinner in New York in October after their third debate.
A similar situation unfolded in 2001, when outgoing Vice President Al Gore attended the inauguration of George W. Bush. Gore won more popular votes in their contest, but Bush got more electoral votes.
George H.W. Bush, 92, and Barbara Bush, 91, are "simply not able to attend" the inauguration because of their age, their spokesman Jim McGrath told ABC News.
McGrath noted that they did not attend the 2013 inauguration of Barack Obama either.
ABC News' Shushannah Walshe contributed to this report.