Hall, 55, is recovering at his home in upstate New York and is expected to make a full recovery, publicist Jonathan Wolfson said Wednesday.
Lyme disease is caused by the bite of infected deer ticks and can cause arthritis, neurological problems and encephalitis, a potentially fatal brain inflammation. Early signs include a red bulls-eye rash that slowly expands and flulike symptoms.
"We are so sorry to disappoint our fans, but we promise to make it up to them," Hall said in a statement.
This month's shows have been postponed, but those scheduled for August and September are expected to go on as planned, Wolfson said.
Hall and Oates are known for their 1980s hits including "Maneater," "I Can't Go for That (No Can Do)" and "Kiss on My List."
They have been touring in support of their latest album, "Our Kind of Soul."