The migrants who were brought to safety in Palermo had been travelling on several different boats and were rescued over the weekend, the aid group said.
"Five dead is more than just a number. One was this child's mother," MSF said on its Twitter account, underneath a photograph of a little boy playing on a ship's deck.
The victims, four women and one man, were found dead on a boat that was rescued on Saturday with 112 people on board. They died, according to initial tests, as a result of dehydration.
Two other passengers found in a critical state were recovering, MSF said in a statement.
Shocked survivors said their rickety boat had only left Libya's shores for Italy 13 hours before they were rescued. In that short time, five of the children on board lost a parent.
Loris De Filippi, president of MSF Italy, warned that any delay in migrants' rescue could be a matter of life or death, as he reiterated calls on Europe to open up new, legal routes to allow migrants and refugees in.
More than 1,900 migrants have died this year making the dangerous journey across the Mediterranean to Europe, out of around 150,000 people who have made the crossing, the International Organization for Migration said last month.