NDVI is categorized in greenness indices which means that it is more appropriate to infer vigor of green vegetation and is known to some problems. In other words, it does not strictly reflect crop growth rate, but might be related. I would suggest use of a canopy nitrogen index such as NDNI, since high nitrogen concentrations generally present a quick growth rate.

See this for more information:

Serrano, L., J. Penuelas, and S.L. Ustin, 2002. Remote Sensing of Nitrogen and Lignin in Mediterranean Vegetation from AVIRIS Data: Decomposing Biochemical from Structural Signals. Remote Sensing of Environment 81:355-364.

I would also agree with U, on the fact that NDVI is basically a measure of grenness. However it has a strong correlation with green biomass, which is indicative of growth. Observing the timeseries NDVI images shows the growth / increase in biomass accumulation. The rate of increase in the time series curve of NDVI has also indicate the plant growth rate. So it is profoundly used as an indication of green growth/plant growth.

I agree that NDVI indicative of canopy greeness and health. However it is being used in NPP. So it can be used to estimate crop growth rate provided we have time series data and establish relation first using test sample

Read more about land surface phenology (de Beurs and Henebry 2004a). It is a study of recurrent biological activities of crops like the start of season, onset of greeness etc. It uses low resolution satellite images like MODIS which have good temporal resolution, which comes with data products like NDVI and EVI and can be used to extract good time series, that indicate plant growth.

Reference

de Beurs KM, Henebry GM (2004a) Land surface phenology, climatic variation, and institutional change: analyzing agricultural land cover change in Kazakhstan. Remote Sens Environ 89:497–509, doi:10.1016/j.rse.2003.11.006

NDVI is quite limiting as it is vased on NIR and red only, well it is well known that other bands are involved in crop growth detection. See Mariotto et al., 2013 in RSE, and papers from P. Thenkabail.

NDVI is an instantaneous measurement of the product of path independent processes.  From a thermodynamic point of view, there are an infinite number of paths that could produce the same measurement basically because you have so many unknown variables.  Your question actually is about those unknown values and determining them.  What processes produce a strong red edge (the basis for NDVI)?  I suggest you investigate places where there is significant control over plant growth that you can measure with remote sensing.  Then perform some level of sensitivity analysis to extract the most dominant characteristics.  For the statistically impaired like myself, decision trees with bagging and boosting, and neural networks are places to start.   See the WEKA machine learning workbench to find out about these methods. 

NDVI is a very common index but it has some limitations (nothing is perfect;~)).

The main one is lack of sensitivity when related to some plant parameters when the LAI or biomass goes above a certain threshold. 

since as mentioned above growth rate might be related to LAI I do suggest looking at REIP. in this paper there is a comparison between NDVI and REIP for LAI assessment in 2 crops. 

Herrmann, I., Pimstein, A., Karnieli, A., Cohen, Y., Alchanatis, V., & bonfil, D., J. (2011). LAI assessment of wheat and potato crops by VENμS and Sentinel-2 bands. Remote Sensing of Environment, 115, 2141-2151

if there is a need to asses nitrogen there are  indices based on direct and indirect relation to nitrogen that are presented in this paper. 

Herrmann, I., Karnieli, A., Bonfil, D., J., Cohen, Y., & Alchanatis, V. (2010). SWIR-based spectral indices for assessing nitrogen content in potato fields. International Journal of Remote Sensing, 31, 5127-5143

goodluck

NDVI can  indicate the  phenology for crop growth, NDVI abnormal can show  the  phenology abnormal.

NDVI is affected by amount of vegetation it has to be carefully calibrated, therefore, if to use it for phenology all parameters are to be the same (crop, seeding, irrigation........).

My experience from a case study measure leaf area index using NDVI produced low correlation (R2 less than 30%) but it is relatively higher as compared to leaf nitrogen level of frond 17 versus NDVI (R2 less than 10%). NDVI is a measure of greenness but it only reflect the upper canopy greenness of oil palm, and not represent the leaf nitrogen status of entire canopy of oil palm (represented by frond 17).

Need calibration from large dataset collected from all growth stages and various site variabilities. NDVI alone may not be the best predictor.

Its help to analyse the crop phenology along with their condition.

To achieve better nitrogen assessment try the NRI1510 presented in --> 

https://www.researchgate.net/publication/252110620_SWIR-based_spectral_indices_for_assessing_nitrogen_content_in_potato_fields

Article SWIR-based spectral indices for assessing nitrogen content i...

i will agree with amir