Micheál Martin will join the President of the European Parliament, Roberta Metsola, in unveiling the bust later.
Mr Hume, a founding member of the SDLP, was one of the highest-profile politicians in Northern Ireland.
He died in Derry in 2020.
The former MEP was also a key architect of the Good Friday Agreement in 1998.
The sculpture was created by Irish artist Liz O’Kane and has been donated to the European Parliament by the Irish government.
During his two day trip, Mr Martin will also meet representatives of the Council of Europe to mark Ireland’s presidency of the body from May to November of this year.On Wednesday, the Taoiseach will address the European Parliament, reflecting on 50 years since Ireland decided to join the European Union.