The home side, looking to rebound after losing 2-1 to Turkey on Thursday, took the lead in the 14th minute when Marcus Berg converted a cross with a first-time effort past Czech goalkeeper Tomas Vaclik.
The Czechs, who lost to Scotland 1-0 at home last week, levelled in the 26th minute through Matej Vydra's diving header.
The Swedes controlled much of the game and created a number of chances throughout, forcing Vaclik into several sharp saves.
They also welcomed the return of Ibrahimovic, who missed Sweden's friendly against Turkey.
Striker Ibrahimovic, 34, recently secured his fourth Ligue 1 title with Paris St Germain and scored 11 goals in Euro 2016 qualifying for the Swedes.
Czech manager Pavel Vrba used a number of young players as he continues to experiment with different lineups ahead of this year's tournament.
The Czechs left Borek Dockal -- their leading scorer during qualifying -- on the bench for most of the match and played without injured Arsenal duo Tomas Rosicky and Petr Cech.
Sweden have been drawn in Group E with Ireland, Italy and Belgium for the Euro 2016 finals in France in June and July.
The Czechs, who finished top of their qualifying group ahead of Iceland, Turkey and the Netherlands, will begin their Euro 2016 campaign with a Group D match against holders Spain.
(Reporting by Michael Kahn, Editing by Toby Davis)
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