jsdoc two dimensional array

Louis answer is valid, but the maintainer updated the repository and now also the code you provided is valid:

@type {string[][]}

According to what the current maintainer of jsdoc says in this issue report, as we speak jsdoc 3 cannot handle declaring multidimensional arrays by adding square brackets. You can do it like you did with Array.<string[]>, or with Array.<Array.<string>>.

According to the issue report, version 3.3.0 will allow the notation you wanted to use.