It happened at 55th and Kedzie in the city's Gage Park neighborhood.
A customer received the most serious injuries. A store manager and another employee were also hurt.
Police say the attack appears to be a random act of violence. The suspect is in custody, but investigators still have no motive.
One female customer who suffered critical stab wounds underwent surgery Tuesday morning at Mount Sinai Hospital. Family members have not released any information about her condition.
"Things are getting worse...It is getting kinda rough in this area," said Guillermo Zamudio.
The stabbings happened around 1 a.m. Tuesday morning.
Officers say they arrested the offender as he left the store and recovered a knife from the scene.
"Everybody's gotta be careful nowadays. The climate is hot and everybody's out here now, so just watch out and be careful," said Oswaldo Andrade.
By Tuesday afternoon, things had returned to normal at the 24-hour Walgreens, although police were still on the premises investigating.
A Walgreens spokesperson said they are working with authorities but will not comment on the incident.
"This happens all the time. Like last week right where I work, he got killed, like two guys, so I'm not surprised by this," said Denaro Mendez .
Mendez has lived and worked in the area for some time and says it is now time to leave.
"That's the reason I've got to try and find another job in another place. This neighborhood is dangerous," said Mendez.
A police news affairs spokesperson said she could not believe the senselessness of this crime.
Longtime Gage Park residents say they now walk the streets in fear. They want more police presence in their community.