Officers say they believe the series of incidents, affecting businesses in the town centre, are linked.
The crimes are reported to have happened between 8pm on Monday, June 24, and 9am on Tuesday, June 25, at businesses in High Street, Manor Walk and Church Square.
Entry was gained at a premises in Church Square where a quantity of cash was stolen. In the other offences, attempts were made to break in but no entry was gained.
Officers said they believe the offences are linked due to the close proximity and times.
Sgt Gurpreet Mulley from Harborough neighbourhood team, said: “Officers have been providing extra patrols in the area and would like to reassure those business owners affected that these reports are being actively investigated.
"We would like to ask anyone who have been in the area and may have witnessed anything related to these offences to get in touch. Did you see anyone in the area acting suspiciously? Did you notice something which may be connected to these offences? If so, please call us.
"We would also like to ask businesses in the local area to review their CCTV to see if they have captured anything related to these reports or ultimately may have been targeted themselves and haven’t as yet reported it to police.
"Anyone with information is asked to contact PC 4234 Ian Kilpatrick on 101. Alternatively you can private message the Leicestershire Police Facebook page."