Johnson was driving home early Thursday when he felt light-headed and parked his car near his home, according to a police statement.
Officers found him after a passerby called 911 to report that a person was sleeping on a stop sign.
"Responsible officers arrived at the scene and checked the well-being of the chief. Officers do not observe any signs of harm and the chief goes home, "the police said. Johnson was not tested for sobriety.
"He revealed to me that he had had several drinks with dinner," Lightfoot said, noting that she did not specifically ask Johnson if he had been drinking.
When CNN contacts the mayor's office, its employees refer to an interview with the newspaper.
Speaking to reporters Thursday, Johnson said he felt his blood pressure rise when he decided to park his car.
Johnson says he was prescribed medication after receiving a blood clot in the summer. He said he felt unwell on Thursday as his doctor changed his medication earlier in the week but accidentally missed taking it.
He saw a doctor Thursday because of problems with his blood pressure, police said.
Not required to take a sobriety test
An internal investigation of the incident is being conducted at Johnson's request.
"The chief commenced this investigation because, as he put it," whether you are a police officer or a police officer, all officers must be held to the highest standard, "police said in a statement.
Asked by The Sun-Times why the chief was not given a field sobriety test, Lightfoot declined comment and said he did not want to "evaluate" the internal investigation.
"I know what my boss said to me, which means he had some medical problems this week, he changed medication, didn't feel well, pulled away. And then IAD will do the rest." [1
"If someone sleeps in a car, it does not mean that they are impaired in any way," Johnson says.  A Chicago police spokesman said there were no reports of misconduct.
"While there are no indications of unlawfulness at this time, this question can only be answered by an internal affairs investigation. This investigation [is] is ongoing and ongoing, "the spokesman said.
Amanda Watts of CNN contributed to this report.