One victim was a 9-year-old girl knocked down by a concrete wall at her elementary school as she walked by.
Local police said a girl, aged nine, had died in the city of Takatsuki, north of Osaka city.
Japanese government spokesman Yoshihide Suga said there were no reports of major damage as of 8.30am (local time). The initial strength of the quake was measured at 5.9.
Senior government officials are gathering for an emergency meeting at the Prime Minister's office, broadcaster NHK reported.
The Yomiuri Shimbun An estimated magnitude-5.9 quake occurred in Osaka Prefecture at about 7: 58 a.m. Monday.
Trump claims he has 'largely solved' North Korea problem
Donald Trump said he wishes people would "sit up and pay attention" to him the way they do in North Korea when Kim Jong Un speaks. Don't let anyone think anything different.
Kansai Electric Power said no irregularities had been detected at the Mihama, Takahama and Ohi nuclear plants after the quake.
Kate Kilpatrick, visiting Japan for the first time from the United States, said alarms went off nearly immediately in the Osaka hotel she was staying and a loudspeaker told guests to stay away from windows.
Takuya Nishimura, an associate professor of geodetics at Kyoto University, said there was a possibility that the quake had occurred at the eastern end of a fault extending from the northern part of the prefecture to Awaji Island in Hyogo Prefecture. The Meteorological Agency warned, however, that aftershocks could be felt over the next two to three days. The strongest shaking was in an area north of Osaka city, the agency said.
Several rail services were suspended, including the bullet train. "Almost all of the dishes fell and shattered on the floor", said Kaori Iwakiri, a 50-year-old nurse in Moriguchi, just north of Osaka city.
Singaporean Benny Tong, who is in Osaka to visit his fiancee and her family, said he felt "intense rattling" for about 20 seconds before the quake.