Video showed loud bangs as lines of officers penned in a group of demonstrators, many wearing black hoods or face masks, who had earlier smashed shop and car windows.
People could be seen running from downtown Washington with their arms held up as the riot police moved in.
Around 150 protesters were thought to be involved in clashes at a Bank of America branch and a McDonald’s restaurant before the inauguration ceremony.
The group chanted “hands up, don’t shoot” as they were cordoned off.
More than 90 have been arrested during the clashes and two police officers have been injured. Reports said some protesters had broken up chunks of pavement to use as missiles.
Sky News US Correspondent Hannah Thomas-Peter, speaking from the scene in downtown Washington, said a large line of police officers were moving the protesters away and said a National Guard Humvee was at the site of the clashes.
She said: “This is turning into a bit of a nightmare for the police.”
Demonstrators wearing orange jumpsuits with black hoods over their faces – representing prisoners in the US detention facility at Guantanamo Bay – were earlier at one security checkpoint before the ceremony.
Other groups including Black Lives Matter and feminist organisations were among other protesters ahead of the ceremony.
More demonstrations are expected to take place as the inauguration continues, including a DisruptJ20 march from Columbus Circle outside Union Station to McPherson Square three blocks from the White House.
Filmmaker and liberal activist Michael Moore will feature in a rally at the square.
Alli McCracken, 28, DisruptJ20 protest organiser, said the demonstrations were over Mr Trump’s comments about women, immigrants and Muslims.
She said: “We have a lot of people of diverse backgrounds who are against US imperialism and we feel Trump will continue that legacy.”
The ANSWER Coalition anti-war group is planning to stage demonstrations along the parade route.
Supporters of Mr Trump lined up at checkpoints before dawn to take their places along the route of the parade, with cheers heard as he and wife Melania arrived at the White House, where he met with Barack Obama.
Some of the demonstrations attempted to block access to the checkpoints.
Clashes took place on Thursday evening outside the National Press Club in central Washington DC, with police using chemical spray to disperse protesters.
Further protests are planned for Saturday, when a massive Women’s March on Washington will take place.
Demonstrations on Inauguration Day are not unique to Mr Trump’s candidacy.
Richard Nixon’s first and second terms drew memorable protests, with demonstrations over the Vietnam War before his second stint in the White House.
During President George W Bush’s inauguration in 2001, demonstrators turned their back as the president passed by along the parade route, with others holding signs including “Hail To The Thief” in reference to his election over Democrat Al Gore.