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No, there is no minimum amount that does not have to be reported. Yes, the income should be included in the tax return.

It sounds as though your wife is considered clergy or a minister/evangelist.

If your wife is a minister then the gross amount should be entered in to box 1 of the W-2. For a clergy/minister the church is not a withholding agent for the social security and medicare tax.  Instead, the clergy/minister employee is considered common law and must report the income and pay the taxes as though they were self employed. 

The basics of this type of situation is that the church, under the tax law and employer tax laws, specific to clergy/ministers (not other employees) is not required to pay the employer share or the employee share of those taxes.  The also do not have to withhold federal income tax but they do have an option if they choose.

Minister Data Entry - Most Common (steps 1-6)

1. Enter/Import the Form W-2
2. If housing allowance is printed in box 14
   1. Disregard it and do not enter it in box 14
   2. Check the import to delete it from box 14 if necessary
3. After entering the Form W-2, answer the question about "uncommon situations" by selecting "Religious employment"
4. Continue Select "You earned this income for clergy employment > Continue
5. Enter the amount of the housing allowance, if applicable, and the amount of qualifying expenses (use the "Learn More" hyperlink to see the qualifying expenses).
   1. If all of the housing allowance is not used for qualifying expenses any excess will be included in taxable income on the tax return - TurboTax will calculate this based on your entry.
6. The most common response to "Clergy Self-Employment Tax" is "Pay self-employment tax on wages and housing allowance" unless a Form 4361 is on file with the IRS.