Moises R. Trevizo has been charged with unlawful possession of explosives and has been cooperative with police and clinic workers, said Capt. Doug Nolte.
Trevizo and his attorney couldn't be immediately reached for comment.
The explosive device was several fireworks that the suspect put together, police said.
"It was dangerous. Don't get me wrong. But it was the size of a salt shaker," Nolte told CNN.
Police don't think the suspect planned to do anything against the clinic, Nolte said.
The suspect had just moved out of a house and carried all his possessions in the backpack, police told CNN affiliate KSNW.
The suspect said a friend had made the device, the station reported.
The incident occurred Monday afternoon at South Wind Women's Center, which is located in the same facility once occupied by Dr. George Tiller and his clinic, which provided abortions. Tiller, 67, was killed in church by an anti-abortion gunman in 2009. Tiller was one of the few U.S. physicians who performed late-term abortions.
South Wind Women's Center was open for business Monday with doctors and patients, said Julie Burkhart, who founded Trust Women Foundation, which opened the clinic. Burkhart had worked for Tiller for seven years.
"With what happened with him and other instances of violence across the country, we enacted security protocols," Burkhart said, referring to Tiller and violence against other abortion clinics.
"I'm very concerned that someone would come in the building with weapons. He was carrying knives and explosives. This really illustrates to me that the security protocols that we have in place work," Burkhart said.
South Wind Women's Center even holds frequent drills with staff, Burkhart said.
"We don't let people just walk in with backpacks without searching them," Burkhart said.
This year, abortion providers are being targeted by an increasing number of hostile and criminal actions ever since an anti-abortion group released a series of videos purporting to show Planned Parenthood engaged in the selling of fetal organs for profit. Planned Parenthood has denounced the videos.
"Since the first heavily edited video was released on July 14th, we've seen a dramatic escalation in harassment, hate speech, stalking, threats, and criminal activity," said Vicki Saporta, president and CEO of the National Abortion Federation
"Anti-abortion extremists have even offered rewards online for the murder of two individuals," Saporta said in a statement. "We are concerned about this escalation and have brought these threats and criminal activities to the attention of law enforcement."
Overall, incidents of violence against abortion providers dropped last year, to 99 such cases from 299 in 2013, the National Abortion Federation said.
Of those 99 incidents, 78 were trespassing cases.
Incidents of disruptions against abortion providers also fell last year, to 6,121 from 6,484 nationwide, the federation said. Picketing makes up nearly all those incidents, followed by hate mail and harassing calls, the federation said.