Spreadsheets are commonly used by non-programmers to store data in a structured form, this data can in some cases be considered to be a program in a domain-specific language (DSL). Unlike ordinary text-based domain-specific languages, there is however currently no formalism for expressing the syntax of such spreadsheet-based DSLs, and there is no tool support for automatically generating language infrastructure such as parsers and IDEs. In this paper we define a simple notion of two-dimensional grammars for spreadsheet-based DSLs, and show how such grammars can be used for automatically generating parsers that extract structured data from a spreadsheet in the form of an AST. We demonstrate automatic generation of parsers for a number of examples, including the questionnaire DSL programming challenge and a DSL for writing safety specifications.