It's a step toward building a relationship with the new Republican commander-in-chief, Pugh spokesman Anthony McCarthy said Wednesday.
Pugh is one of "hundreds of mayors" invited from across the country, he said.
"He is the president of the United States," McCarthy said. "We are looking forward to developing a relationship with the Trump administration that would benefit infrastructure here in the city of Baltimore as well as for other opportunities for us to continue to meet the most critical needs of the citizens of Baltimore."
The mayor also plans to participate in several inaugural events in Washington that evening. McCarthy did not provide details on which events she would attend.
Maryland Republican Gov. Larry Hogan, who did not vote for Trump, also plans to attend the inauguration.
Two Democrats in Maryland's congressional delegation have said they'll skip it. Reps. Anthony G. Brown and Jamie Raskin announced their plans after Trump criticized Democratic Rep. John Lewis of Georgia, a civil rights icon who was among the original Freedom Riders. Trump's criticism on Twitter came after Lewis, in an interview, questioned the legitimacy of Trump's election victory.
Baltimore, like Maryland, is overwhelmingly Democratic. Hillary Clinton, the Democratic nominee for president, won about 60 percent of the vote in Maryland — one of her strongest showings in the general election.
Pugh, however, has identified several areas where she sees Trump as a potential ally.
In one of her first acts as mayor, Pugh approached Trump at the Army-Navy football game at M&T Bank Stadium. She handed him a two-page letter that stressed the city's need for federal infrastructure funding — including for redeveloping Port Covington, expanding the Howard Street tunnel, upgrading water pipes and building new broadband.
The president-elect has outlined plans to spend $1 trillion improving the nation's infrastructure.
McCarthy said Trump had not sent Pugh a formal response to the letter. The Trump transition team did not respond to a request for comment Wednesday.
Pugh approached Trump in December as he stepped out of his vehicle at the stadium. During the brief exchange, she welcomed him to Baltimore and told him she wants to be the "model city down the street" when it comes to new infrastructure spending. Pugh also gave Trump a Baltimore pin as a reminder of the city's needs.
At the end of their encounter, Pugh said Trump told her, "That's good. Let's take a picture."
The Baltimore City Council voted last month to condemn Trump's rhetoric, calling it divisive, scapegoating and rooted in hate and prejudice. Supporters said the resolution was a way to affirm the city's values.