It looks like this would be it. Here are the closest other calls I could find.
The 1960 National Champions won their first 7 in a row, having lost the last game of 1959, but then lost 23-14 to Purdue.
The 1961 team won 7 in a row sandwiched between a 6-0 loss to Missouri and a 23-21 loss to Wisconsin.
The 2001 team beat Wisconsin 42-31 in the season finale and then started 2002 with 4 consecutive wins, then lost to a decent Purdue team 28-15, and followed it with 3 more consecutive wins before getting demolished by Ohio State 34-3. That was 8 wins in 9 games and it could have been 9 in a row before running into Ohio State. We led Purdue at the half.
We finished 2002 with a Music City Bowl win over Arkansas and then started 2003 with 6 straight wins. The 7 game winning streak ought to have been 8, but then the infamous Michigan collapse happened. We lost the next week by 6 to Michigan State in a game we fell behind in 17-0 while still shellshocked from the week before but then climbed back into and nearly won. Then we won 3 in a row before losing comprehensively to Iowa. Granted there are some big ifs and dominos that would need to fall, but beat Michigan and Michigan State and the Gophers could have been looking at a 12 game win streak.
The 2003 team had a hand in both of the longest streaks since 1961 prior to the current one. In addition to the 7-gamer ending in the Michigan collapse, they started a 6-gamer by beating Oregon in the Sun Bowl. That streak also was snapped by the Wolverines with a 4th quarter comeback.
The school record is 24, from 1903 to 1905. That string of wins followed the 6-6 tie with Michigan in the Little Brown Jug origin game, all part of a 35 game unbeaten streak.