The 85-year-old conservative is in a clinic in the south-western city of Heidelberg, Der Spiegel reports.
His office said he was "doing well under the circumstances".
The so-called "father of reunification" was modern Germany's longest-serving chancellor, coinciding with the peaceful end of the Cold War.
He served as chancellor from 1982 to 1998.
Der Spiegel described his condition as "critical" (in German), quoting sources close to the former chancellor. It said he had been in intensive care for the past three weeks.
According to Bunte magazine, Mr Kohl was unconscious for a long time following the intestine operation.
The statement from his office said he had a successful hip replacement in May, but then required another operation, without saying what.
Mr Kohl is credited with bringing East and West Germany together after the fall of the Berlin Wall and - together with his French ally President Francois Mitterrand - was responsible for the introduction of the euro.
Former US President George Bush Senior once described him as the most important European leader of the late 20th Century.
In more recent years, the former chancellor has been a frail figure and he has rarely been seen in public although he has spoken in support of closer European integration, says the BBC's Jenny Hill in Berlin.
Mr Kohl fell from grace when a funding scandal under his leadership of the Christian Democrats came to light after he left office in 1998.
Current Chancellor Angela Merkel was once a protegee of Mr Kohl, first entering government under his rule in 1991.
But she publicly denounced Mr Kohl and called for his resignation when it was revealed the party had received millions of dollars worth of illegal donations using secret bank accounts.
In 2011, in a series of interviews and statements, he spoke out against Mrs Merkel's policy of strict austerity to deal with the European debt crisis.
Mr Kohl, who exited active politics in 2002, has been confined to a wheelchair in recent years after suffering a stroke.
Former German chancellor and architect of reunification Helmut Kohl is in intensive care after surgery on his intestine, German media reports say.