Hi ApurvaShah,
You can use “Open with Explorer” option to move your data to the SharePoint Online library keeping the folder structure. However, considering the speed and automation, I recommend you first sync the SharePoint Online library to the local drive and then move your data with folders altogether to the synced folder. They will automatically sync to the cloud whenever you’re online. Please note the speed would be affected by the network speed.
Here are two articles about “Open with Explorer” and OneDrive for Business sync for your reference:
http://support.microsoft.com/kb/2629108
Thanks,
Mills Fan