The Danes are in the Swedish capital as part of their World Cup preparations, but Tottenham player Eriksen, who netted eight goals for his country in qualifying, did not make the journey.
"It (the baby) was due yesterday, and he stays home in Odense and meets us on Tuesday again if nothing happens. He's on standby for that," Hareide said at a media conference at Stockholm's friends Arena.
The Danes face Mexico in their final friendly at Brondby Stadium in Copenhagen on June 9 before heading to Russia, where they open their World Cup Group C campaign against Peru on June 16 before facing Australia and France.
The Swedes will be missing striker John Guidetti, who injured an ankle after getting on the wrong end of a heavy tackle from team captain Andreas Granqvist in training on Thursday.
Janne Andersson's side will meet Peru in Gothenburg before they depart for Russia, where they will fight it out with South Korea, Germany and Mexico in Group F.
(Reporting by Philip O'Connor; Editing by Hugh Lawson)
