Move top 1000 lines from text file to a new file using Unix shell commands

head -1000 input > output && sed -i '1,+999d' input

For example:

$ cat input 
1
2
3
4
5
6
$ head -3 input > output && sed -i '1,+2d' input
$ cat input 
4
5
6
$ cat output 
1
2
3