Obtain the land cover data for the location and year(s) that you are interested in from the USGS site:
https://lpdaac.usgs.gov/dataset_discovery/modis/modis_products_table/mcd12q1
Data are distributed in the Hierarchical Data Format (HDF) and each file contains multiple layers of data. While you can open this file directly in ENVI, this will not retain any coordinate information. You should use the MODIS Conversion Tool Kit (MCTK) found under the Toolbox | Extension | MCTK.
Select the HDF file then pick the data layer(s) you are interested in. Unless you plan to mosaic multiple tiles, choose Reprojected Rigorous georeferencing under the Select Output Type section. In the right-most panel that opens select Geographic Lat/Lon and enter 255 for the Background Value to Use. Enter an Output Path and Rootname and click the Process button.
When the data are imported ENVI will not recognize this file as a classified image. You can use the ENVI tools to edit the header file but it will be much simpler to modify this with a text editor. Make a backup copy of the ENVI header file that you have just created, the file with the .HDR file extension. Now open the original header file with a text editor and paste the contents of the IGBP-Class-Info.txt file at the end of the header file. Save the header file then use the ENVI Data Manager to close the file. Reopen the file in ENVI and it will be recognized as a classification image, with the appropriate Class names and colors, and the Data Ignore value will be set to 255. You can use this same IGBP Class file for the University of Maryland Type 2 classification scheme.
If you have already imported these data following the MODIS Land Cover data in ArcGIS FAQ you can simply open the TIF file in ENVI. If you used ArcGIS to reproject the raster from sinusoidal to Geographic then ENVI will recognize the coordinate system.