The 36-year-old athlete, who won bronze in the 5,000m at the 1992 Barcelona Olympics, was caught on Monday hours after the incident took place in Alem Gena - six kilometres west of the capital.
Police declined to give further details when contacted by AFP, but a local newspaper said the couple, who have five children, were embroiled in a legal battle over the ownership of a kindergarten school.
The paper said the un-named wife remained in a stable condition in a hospital in Addis Ababa.
Bayisa also won silver at the 1991 World Athletics Championships in Tokyo.
He finished fourth in his last competition, the 2000 Sydney Olympic Games. -- AFP