Police spokesman Henning Svendsen said officers responded to the man's home in Birkeroed, north of Copenhagen, after receiving a pre-dawn call from his estranged wife.
She had become worried by a text message from the man saying he would take the children "on a journey," Svendsen said.
The couple had split custody of the children.
When police arrived at the father's home, they found two boys, aged 2 and 10, and an 8-year-old girl shot dead, Svendsen said. The father was conscious but sick, apparently from an overdose of sleeping pills. Police believe he tried but failed to kill himself after the attack.
Police declined to identify him in line with Danish privacy rules.