Clinton canceled her next appearance in Fort Worth, telling about 2,000 people who had gathered outside the Tarrant County courthouse that it would be inappropriate to campaign in the wake of the accident.
Killed was 20-year Dallas police Officer Victor Lozado, who had a wife and four children, two of them in college.
"It is important that we respect and appreciate their service," she said. "I certainly am grateful for all they do for me."
Police Chief David Kunkle said Clinton had called to offer her condolences to Lozado's widow and fellow officers.
Lozado died after apparently crashing into a concrete barrier along a viaduct near downtown Dallas, said Lt. Vernon Hale, a police spokesman. Aerial video showed wreckage scattered for several yards.
The officer was in the rear of the motorcade, following it as it took a turn not far from Dealey Plaza, where John F. Kennedy was assassinated in 1963.
Asked if police had enough lead time to plan a safe route, Hale said, "It doesn't matter with our guys. They've been doing this so long. Of course, we already had one tragedy in Dallas."
Kunkle, accompanied by Dallas Mayor Tom Leppert at the hospital, said the motorcades involve intricate driving.
"The motorcycle escorts we do are very dangerous. They require officers to speed up and ride ahead of the motorcade and set up, and do that over and over again. So there's always an element of danger to these motorcades, but the accident is still under investigation."
In August 2006, an Albuquerque, N.M., police officer in President Bush's motorcade died in a motorcycle crash. Germaine Casey, 40, died on Aug. 27 when he crashed as Bush returned to the airport after a fundraiser for Sen. Pete Domenici, R-N.M.
In November 2006, Honolulu police Officer Steve Favela died when he and two other motorcycle officers crashed while part of a presidential motorcade.
