The guitarist and singer had “enthralled his teeming followers” during a career of more than 64 years, Mr Jonathan said.
Fatai was best known for his song, They Cannot Match Us, which criticised younger generations.
The exact cause of Fatai’s death, or his age, is not known.
He died after more than 10 days in a coma, and was aged either 85 or 87, Nigeria’s This Day newspaper reports.
In highlife’s golden era in the 1950s and 1960s, Fatai, whose real name was Fatai Olagunju, was a nationally celebrated performer.
Mr Jonathan believed the vacuum his death has created in the Nigerian entertainment industry will be hard to fill, his statement said.
Highlife music, born in West Africa, is similar in sound to Caribbean calypso and often satirises modern life.
In an interview with AFP new agency more than a year ago, Fatai bemoaned the hip-hop music that now dominates in Nigeria.
He said “a good musician should know how to play any instrument”, showing his irritation with artists he accused of sometimes being “lazy” and simply seeking “easy money”, AFP reports.