The incident occurred shortly before midday.
Neighbours have been complaining to the police about suspicious activities in the area.
Fifty-seven of the 78 Palma neighbourhoods registered an increase in average income in 2016.
At one point the man nearly dropped the baby on the ground.
Several streets were cordoned off when the operation started at five in the afternoon.
Damage to police vehicles is put at half a million euros.
Over 100 armed police officers were involved in the evening raid against drugs and illegal immigration.
The robberies were in Palma, Bunyola, Calvia and Marratxi.