Stockholm dominates the statistics with 38 cases reported in the capital since the law came into force on October 1st, according to a report by TV4 Nyheterna news programme.
"It shows that the legislation was needed," said prosecutor Mary Thorell in a statement.
The new law enabled victims of stalkers to report successive incidents under the new charge of unlawful persecution (olaglig förföljelse).
Previously alleged victims had been obliged to report each incident as an individual case of threatening behaviour or assault.
The first trial involving a case of stalking opened on Tuesday in Borås in western Sweden and will serve as an examination of the new law.
The majority of the cases represented in preliminary National Crime Prevention Council (Brottsförebygganderådet - Brå) statistics for October are women - in 60 cases, it concerns adult women, while in five cases the alleged victims are girls aged under 18.
According to a Brå study from 2006, one in ten Swedes has experienced some form of stalking at some point in their lives. The majority of those affected are women.
According to the study, the victim is acquainted with the perpetrator in the majority of cases but in a third of all incidents the stalker is an unknown person.