One recent commenter suggested that it does command composition of songs for worshipping God. We'll see, shortly, that it does not. First, let's see what it actually says:
Colossians 3:16 Let the word of Christ dwell in you richly in all wisdom; teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord.
And here is the parallel passage in Ephesians:
17Wherefore be ye not unwise, but understanding what the will of the Lord is. 18And be not drunk with wine, wherein is excess; but be filled with the Spirit; 19Speaking to yourselves in psalms and hymns and spiritual songs, singing and making melody in your heart to the Lord;
As a lexical-grammatical issue, it is important to recognize that psalms, hymns, and spiritual songs are three of the categories of the Psalms from the Greek Psalter (see more detail here).
Once we recognize that fact, these passages become rather clearly exhortations to use the Psalter wisely in teaching and admonishing one another, as well as for song to God. The point is that the Psalter not only worships God but edifies the brethren, as indeed it does.
There is nothing in the verse about writing or composing previously non-existent songs. The word "to write" or any equivalent thereof is simply absent from the text.
An interpretation that the verse must refer to composition of new works of song is simply an example of reading back into the text our own modern-day practices. In short, it is eisegesis. The wise man teaches and exhorts Scripturally. These verses are a call to the use of Scripture for mutual edification, not call to invent a new Psalter.
May God give us wisdom to give unto Him the worship He desires,