Esri has a toolbar extension called Data Interoperability which when licensed can be used to convert varying formats of data. Unfortunately, the Data Interoperability does not support* MBTiles. Therefore you would have to utilize FME to read/write the MBTile data. The links below provide some further information into Data Interoperability and FME which you may find helpful.
FME is a software application that is developed by Safe Software which can be purchased and downloaded from their site.
Supported Formats with Data Interoperability
FME SQLite MBTiles Reader/Writer https://docs.safe.com/fme/html/FME_Desktop_Documentation/FME_ReadersWriters/mbtiles/mbtiles.htm
*MBTiles in Data Interop are only supported if they are raster only. If there is any vector data contained within the MBTile, then it will not be able to be read by Data Interop.
If the data is in pbf format, it will not be able to be read by Data Interop. MBTiles supports PNG, PNG8, and JPEG data stored as binary blobs in the tiles column. MBTile also supports rasters with up to 4 bands.
But, we have an alternative way to create an MBTiles package.