The calculated distance (air line) between Ingelheim am Rhein and Wiesbaden is approximately 11 miles respectively 18 kilometers.
By car or train, the actual journey to Wiesbaden is certainly longer, as only the direct route (as the crow flies) between Ingelheim am Rhein and Wiesbaden has been calculated here.
Air line (approximately)
18 kilometers
10 nautical miles