The Pope was given the item, combining Catholic and communist symbols, by left-wing Bolivian President Evo Morales.
One Catholic bishop suggested that Mr Morales had sought to “manipulate God”.
But while some reports said the Pope was taken aback by the present, the Vatican has played down any row.
The crucifix was based on a design by Luis Espinal, a Jesuit Priest assassinated in 1980 by right-wing militia to whom Pope Francis paid tribute during his trip.
Bolivia’s communications minister, Marianela Paco, told Bolivian radio: “The sickle evokes the peasant, the hammer the carpenter, representing humble workers, God’s people,” adding there was “no other” motive behind the gift.
There are differing interpretations of Pope Francis’ thoughts on it.
Some reports say the Pope was embarrassed, telling Mr Morales “this isn’t good”.
But the Vatican spokesman, Federico Lombardi, said it was more likely Pope Francis had expressed surprise at the origins of the gift.
“I don’t think I would put this symbol on an altar in a church however,” he added.
The Pope himself has been accused of having Marxist leanings, after mounting strong criticisms of capitalism and inequality.
One of the strongest reactions came from Spanish bishop Jose Ignacio Munilla, who tweeted: “The height of arrogance is to manipulate God for the service of atheist ideologies.”
“This is a provocation, a joke” said Bolivian Bishop Gonzalo del Castillo, quoted by an international news agency.
There was also anger on the Facebook pages of the Catholic News Agency. “One cannot simply combine Communism and Christianity!”, wrote one user, “Evo the arrogant. How can a Hammer and Sickle be non-political?” wrote another.
But one comment read: “This is no insult to Pope Francis, this is in memory of the Jesuit Martyr, who died defending the poor and oppressed of Bolivia.”
He next visits Paraguay, the third and final country on his tour of Latin America.