I found the answer myself; updating in case someone has a similar problem.
MyData = rand(46,5);
Site = randi([1 3],46,1);
MyDataNew = reshape(MyData,size(MyData,1)*size(MyData,2),1); % reshape into one column
MeasureDay = repelem(1:5,[size(MyData,1)],[1]); % new variable with values representing measurement days
MeasureDay = reshape(MeasureDay,size(MeasureDay,1)*size(MeasureDay,2),1); % reshape into one column
Site = repmat(Site,5,1); % reshape into one column
boxplot(MyDataNew,[Site,MeasureDay]); % two grouping variables used together