The incident took place around 2:50pm on Tuesday after the road was shut to high sided vehicles because of high winds.
The lorry toppled over initially causing the northbound road to be shut but both ways has now been shut as a precaution.
Inquiries into the full circumstances of the incident are ongoing.
Police are advising motorists to avoid the bridge and use alternative routes.
It is the second incident to have happened on the crossing since January when the bridge was closed over night after a lorry overturned on the nortbound carriageway.
More to follow...