The Gaisspitze (also called "Geißspitze") is a cone shaped mountain in the Verwall Alps in the Austrian state of Tyrol and north of the municipality Galtür. It has an elevation of  m (AA).
The nearest taller mountain is the Glatter Berg (2866 m), about 1 km north. They are separated via the col Muttenjoch (2620 m).
There are two alpine club huts nearby:
Normal routes to the summits are from both huts via Muttenjoch.