The event comes just over a week after more than 750 people drowned in the Mediterranean's worst migrant tragedy.
The three officials will board the Italian naval ship San Giusto off the coast of Sicily, the EU said in a statement on Saturday.
The officials aim to "assess the situation and help ensure European solidarity for the efforts undertaken to save the lives of migrants crossing the Mediterranean Sea", it added.
The visit is part of a string of meetings that Mogherini has planned, citing "the need for a common effort to address the issue of migration, from tackling root causes to facing the emergencies".
The trip takes place eight days after a shipwreck off the Libyan coast killed over 750 people fleeing war and poverty as they tried, like thousands more, to reach Europe.
Last Sunday's disaster came after two other migrant shipwrecks left up to 450 people dead.
Under pressure to deal with a spike in the number of migrants undertaking the perilous journey to European shores, EU leaders held emergency talks on Thursday and decided to triple funding for the bloc's maritime search and rescue operation.
Brussels also wants United Nations approval for an EU military operation against the people smugglers who organise the hazardous crossings, often aboard overcrowded boats.
Britain and France are set to demand a UN Security Council resolution to take action in Libyan territorial waters.
Mogherini on Sunday said it would not be easy for the EU to secure a UN mandate, or the approval of the Libyan authorities, which have not yet formed a unity government.
Ban meanwhile urged the EU to refrain from resorting to force, saying there could be "no military solution" to the tragedies in the Mediterranean.
"What is crucial is to have a global approach that takes into account the roots of the problem, the security and human rights of migrants and refugees, such as having immigration channels that are legal and regular," Ban said in an interview with Italy's La Stampa daily.
Mogherini will travel to the UN headquarters in New York on Tuesday and meet with US Secretary of State John Kerry in Washington on Wednesday.
Aid groups predict that if the migrant crisis continues unabated, there could be 30,000 deaths at sea this year and Italy will have to process 200,000 migrants landing in flimsy boats on its soil.
Already, more than 1,750 migrants have died in shipwrecks this year - 30 times more than the same period in 2014.
The UN rights chief Zeid Ra'ad Al Hussein last week condemned "callous" EU migration policies, which he said are turning the Mediterranean into a "vast cemetery".