How to fix git repository broken by interrupted git fetch?

find a *.pack.temp in .git/objects/pack in your local repository. Then find an .idx file with same basename, and move both of them away (or remove them, but it is better to be safe than sorry). Rerun git fetch and it should work (well, it did for me).

For example:

% git fetch
error: Unable to find a4fb0b54b2609df8a1ee4b97c268d205fc5bf9f1 under https://www.example.com/~someuser/something.git
Cannot obtain needed object a4fb0b54b2609df8a1ee4b97c268d205fc5bf9f1
error: fetch failed.

% ls -l .git/objects/pack
total 65872
-rw-r--r-- 1 someuser someuser    64072 Feb 12  2014 pack-2e31e66e67d8596f1193bbbc06c87293900c6e45.idx
-rw-r--r-- 1 someuser someuser    16920 Jul 21  2013 pack-3d76e0bf6c67d71913efc0711d56f04c7f79b95d.idx
-rw-r--r-- 1 someuser someuser    62224 Feb 11  2014 pack-74107fa80989df6619479874d94b5f8ed010fd2f.idx
-rw-r--r-- 1 someuser someuser    96552 Oct 30 22:55 pack-bb75633331ea0e74d4d3cb29f7660e1ba00fb899.idx
-rw-r--r-- 1 someuser someuser    73228 Mar  6  2014 pack-de0c1bcf3550cd7a2fd0c5a981bc17d15f1144c0.idx
-r--r--r-- 1 someuser someuser   129144 Feb  2 18:57 pack-ffb25d036dea040923468e2de07023f9b497aeb7.idx
-r--r--r-- 1 someuser someuser 46413554 Feb  2 18:57 pack-ffb25d036dea040923468e2de07023f9b497aeb7.pack
-r--r--r-- 1 someuser someuser   129312 Feb  2 19:10 pack-ffbdfa2c676aaf392ea722cb68eaa87e45af092c.idx
-rw-r--r-- 1 someuser someuser 20450545 Feb  2 19:09 pack-ffbdfa2c676aaf392ea722cb68eaa87e45af092c.pack
-rw-r--r-- 1 someuser someuser   129312 Feb  2 18:36 pack-ffbdfa2c676aaf392ea722cb68eaa87e45af092c.idx
-rw-r--r-- 1 someuser someuser  9863168 Feb  2 18:37 pack-ffbdfa2c676aaf392ea722cb68eaa87e45af092c.pack.temp

% mv .git/objects/pack/pack-ffbdfa2c676aaf392ea722cb68eaa87e45af092c.idx /tmp/
% mv .git/objects/pack/pack-ffbdfa2c676aaf392ea722cb68eaa87e45af092c.pack.temp /tmp/
% git fetch
From https://www.example.com/~someuser/something
   3288ab9..a4fb0b5  master     -> origin/master

Try these commands:

git fsck
git gc