The Marvel themed land is due to open in July, with new rides, restaurants and experiences, while the Mickey and Minnie ride is due to open in 2022 following the Disney World opening earlier this year.
The park hasn't revealed whether the pause on construction will affect the opening dates.
A spokesperson told local media that the decision to stop work on the new rides and the closure of the building sites was in line with direction from government and health officials.
California was the first state in the US to lock down earlier this month, with only grocery stores, pharmacies, banks and petrol stations allowed to stay open.
The theme park closed shortly after.
The Avengers Campus is to feature live stunt shows with all of the Marvel heroes, as well as a Spider Man themed ride, an Ant-Man restaurant and a magic workshop with Dr Strange.
Mickey and Minnie's Runaway Railway ride will be a trackless attraction with animatronic figures and theatrical effects.
They aren't the only rides to be affected by the coronavirus building suspension.
The refurbishment of the Indiana Jones Adventure attraction is likely to be paused, while updates to Space Mountain and Frontierland are also to be stopped temporarily.
Sun Online Travel contacted Disney for additional comment.
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