The pane of glass came from the six-storey 3 Sovereign Square building and fell on Thursday evening. Nobody was hurt.
A Co-op store on the ground floor was closed and cordoned off while police investigated.
Swinegate has now re-opened.
3 Sovereign Square only opened in 2017 and offers Grade A office space. It was developed by Bruntwood and Kier but is owned by Leeds City Council, who bought is for nearly £40million in 2016 as a commitment to investing in the city's economy. It was built on the site of the old Queen's Hall concert venue, which was previously a tram depot. After the hall's demolition, the site was a surface car park. Law firm Addleshaw Goddard are the anchor tenants of the development.