For JUST a schedule with bars indicating time ranges a GANTT CHART is probably what you are looking for.
Gantt Project could do that using a web interface.
Screenshot of Gantt Chart
If you want something more, take a look at
schoolforge
Claroline
Claroline is a Web Based Course Management System. It allows teachers (professors, lecturers...) to create and administer course websites through a browser (Internet Explorer, Netscape, FireFox, Mozilla, ...).
* Publish documents in any format (PDF, HTML, Office, Video...).
* Run public or private discussion forums.
* Manage a list of links.
* Create student groups.
* Compose exercises.
* Structure an agenda with tasks and deadlines.
* Make announcements (also via e-mail).
* Have students submit papers.
* Consult statistics of frequenting and success in the exercises.
ClaSS
ClaSS is the ClaSS Student System.
A complete student tracking, reporting and information management system. ClaSS extends the reach of traditional systems by using the latest in web-application methodologies to include the whole school community. ClaSS aims to be the ubiquitous classroom information assistant for schools.
FET
FET is open source free software for automatically scheduling the timetable of a school, high-school or university. It uses a fast and efficient timetabling algorithm. It is licensed under GNU/GPL
Focus/SIS
Focus/SIS is an incredibly powerful tool for managing student data. Focus/SIS has been implemented by many K-12 districts, private schools, and colleges around the nation as their solution to manage their burgeoning student data and share that data with all the stockholders of the school or district.
Focus/SIS is a project that aims to fulfill all the data needs of private schools, school districts, and colleges in the United States and around the world. It is built upon free, enterprise-level technologies, like Linux, Apache, PostgreSQL, and PHP.
etc...